Search for supersymmetry in events with b-quark jets and missing transverse energy in pp collisions at 7 TeV

Results are presented from a search for physics beyond the standard model based on events with large missing transverse energy, at least three jets, and at least one, two, or three b-quark jets. The study is performed using a sample of proton-proton collision data collected at sqrt(s) = 7 TeV with the CMS detector at the LHC in 2011. The integrated luminosity of the sample is 4.98 inverse femtobarns. The observed number of events is found to be consistent with the standard model expectation, which is evaluated using control samples in the data. The results are used to constrain cross sections for the production of supersymmetric particles decaying to b-quark-enriched final states in the context of simplified model spectra.


Introduction
Many extensions of the standard model (SM) predict that events in high-energy proton-proton collisions can contain large missing transverse energy (E miss T ) and multiple, high-transverse momentum (p T ) jets. For example, in R-parity-conserving [1] models of supersymmetry (SUSY) [2], SUSY particles are created in pairs. Each member of the pair initiates a decay chain that terminates with the lightest SUSY particle (LSP) and SM particles. If the LSP only interacts weakly, as in the case of a dark-matter candidate, it escapes detection, potentially yielding significant E miss T . Furthermore, in some scenarios [3], the SUSY partners of the bottom and top quarks can be relatively light, leading to the enhanced production of events with bottom-quark jets (b jets). Events of this type, with b jets and large E miss T , represent a distinctive topological signature that is the subject of a search described in this paper.
We present a search for new physics (NP) in events with large E miss T , no isolated leptons, three or more high-p T jets, and at least one, two, or three b jets. The analysis is based on a sample of proton-proton collision data collected at √ s = 7 TeV with the Compact Muon Solenoid (CMS) detector at the CERN Large Hadron Collider (LHC) in 2011, corresponding to an integrated luminosity of 4.98 fb −1 . Recent searches for NP in a similar final state are presented in Refs. [4][5][6][7][8]. Our analysis is characterized by a strong reliance on techniques that use control samples in data to evaluate the SM background.
The principal sources of the SM background are events with top quarks, comprising tt pair and single-top-quark events, events with a W or Z boson accompanied by jets, and non-top multijet events produced purely through strong-interaction processes. We hereafter refer to this last class of events as "QCD" background. Diboson (WW, ZZ, or WZ) events represent a smaller source of background. For events with a W boson or a top quark, significant E miss T can arise if a W boson decays into a charged lepton and a neutrino. The neutrino provides a source of genuine E miss T . Similarly, significant E miss T can arise in events with a Z boson if the Z boson decays to two neutrinos. For QCD background events, significant E miss T arises primarily from the mismeasurement of jet p T . A smaller component of the QCD background arises from events with semileptonic decays of b and c quarks.
We interpret our results in the context of simplified model spectra (SMS) [9][10][11][12], which provide a general framework to characterize NP signatures. They include only a few NP particles and focus on generic topologies. We consider the SMS scenarios denoted T1bbbb and T1tttt. Event diagrams are shown in Fig. 1. These two models are characterized by b-jet-enriched final states, large jet multiplicities, and large E miss T values, making our analysis sensitive to their production. For convenience, we express SMS phenomenology using SUSY nomenclature. In T1bbbb (T1tttt), pair-produced gluinos g each decay into two b-quark jets (t-quark jets) and the LSP, taken to be the lightest neutralino χ 0 . The LSP is assumed to escape detection, leading to significant E miss T . If the SUSY partner of the bottom quark (top quark) is much lighter than any other squark, with the gluino yet lighter, gluino decays are expected to be dominated by the three-body process shown in Fig. 1(a) [Fig. 1(b)].
As benchmark NP scenarios, we choose the T1bbbb and T1tttt models with gluino mass m g = 925 GeV and LSP mass m LSP = 100 GeV, with normalization to the next-to-leading order (NLO) plus next-to-leading-logarithm (NLL) cross section [13][14][15][16][17]. These two benchmark models lie near the boundary of our expected sensitivity.
In Sections 2-3 we describe the detector and event selection. Section 4 introduces the ∆φ min variable, used in the evaluation of the QCD background. Our techniques to evaluate the SM background from control samples in data are presented in Section 5. In Section 6 we describe our analysis framework, based on a likelihood method that simultaneously determines the SM background and tests the consistency of NP models with the data, taking into account possible NP contamination of control sample regions. The interpretation of our results is presented in Section 7. A summary of the analysis is given in Section 8.

Detector and trigger
A detailed description of the CMS detector is given elsewhere [18]. The CMS coordinate system is defined with the origin at the center of the detector and the z axis along the direction of the counterclockwise beam. The transverse plane is perpendicular to the beam axis, with φ the azimuthal angle (measured in radians), θ the polar angle, and η = − ln[tan(θ/2)] the pseudorapidity. A superconducting solenoid provides an axial magnetic field of 3.8 T. Within the field volume are a silicon pixel and strip tracker, a crystal electromagnetic calorimeter, and a brassscintillator hadron calorimeter. Muons are detected with gas-ionization chambers embedded in the steel flux-return yoke outside the solenoid. The tracker covers the region |η| < 2.5 and the calorimeters |η| < 3.0. The region 3 < |η| < 5 is instrumented with a forward calorimeter. The near-hermeticity of the detector permits accurate measurements of energy balance in the transverse plane.
The principal trigger used for the analysis selects events based on the quantities H T and H miss T , where H T is the scalar sum of the transverse energy of jets and H miss T the modulus of the corresponding vector sum. Due to increasing beam collision rates, trigger conditions varied over the period of data collection. The most stringent trigger requirements were H T > 350 GeV and H miss T > 110 GeV. The efficiency of the H T component for the final event selection is measured from data to be 86% (99%) for H T values of 400 GeV (500 GeV). The efficiency of the H miss T component is 98% for E miss T > 250 GeV. Appropriate corrections are applied to account for trigger inefficiencies and uncertainties in the various control and search regions of the analysis.

Event selection
Physics objects are defined using the particle flow (PF) method [19], which is used to reconstruct and identify charged and neutral hadrons, electrons (with associated bremsstrahlung photons), muons, tau leptons, and photons, using an optimized combination of information from CMS subdetectors. The PF objects serve as input for jet reconstruction, based on the antik T algorithm [20] with distance parameter 0.5. Jet corrections [21] are applied to account for residual effects of non-uniform detector response in both p T and η. The missing transverse energy E miss T is defined as the modulus of the vector sum of the transverse momenta of all PF objects. The E miss T vector is the negative of the same vector sum. , and the number of tagged b jets N bjets are given. The designations 1b, 2b, and 3b refer to the minimum N bjets value, while "loose" and "tight" refer to less restrictive and more restrictive selection requirements, respectively, for H T and E miss T .

Signal region
The basic event selection criteria are as follows: • at least one well-defined primary event vertex [22]; • at least three jets with p T > 50 GeV and |η| < 2.4; • a lepton veto defined by requiring that there be no identified, isolated electron or muon candidate [23,24] with p T > 10 GeV; electron candidates are restricted to |η| < 2.5 and muon candidates to |η| < 2.4; • ∆φ min > 4.0, where the ∆φ min variable is described in Section 4.
Electrons and muons are considered isolated if the scalar sum of the transverse momenta of charged hadrons, photons, and neutral hadrons surrounding the lepton within a cone of radius (∆η) 2 + (∆φ) 2 = 0.3, divided by the lepton p T value itself, is less than 0.20 for electrons and 0.15 for muons.
To identify b jets, we use the combined-secondary-vertex algorithm at the medium working point [25]. This algorithm combines information about secondary vertices, track impact parameters, and jet kinematics, to separate b jets from light-flavored-quark, charm-quark, and gluon jets. To increase sensitivity to NP scenarios, which often predict soft b jets, we use all tagged b jets with p T > 30 GeV. The nominal b-jet-tagging efficiency is about 75% for jets with a p T value of 100 GeV, as determined from a sample of b-jet-enriched dijet events [25] (for b jets with p T ≈ 30 GeV, this efficiency is about 60%). The corresponding misidentification rate is about 1.0%. We correct the simulated efficiencies for b-jet tagging and misidentification to match the efficiencies measured with control samples in the data. The b-tagging correction factor depends slightly on the jet p T and has a typical value of 0.95. The uncertainty on this correction factor varies from 0.03 to 0.07 for b jets with p T from 30 to 670 GeV, and is taken to be 0.13 for b jets with p T > 670 GeV.
We define five signal regions, which partially overlap, to enhance sensitivity in different kinematic regimes. The five regions correspond to different minimum requirements on H T , E miss T , and the number of b jets. H T is calculated using jets with p T > 50 GeV and |η| < 2.4. The five regions, denoted 1BL, 1BT, 2BL, 2BT, and 3B, are specified in Table 1 and were chosen without considering the data to avoid possible bias. The regions are selected based on expected signal and background event yields in simulation, to provide maximal sensitivity for discovery of the NP scenarios considered in this paper or, in the case of non-discovery, to best set limits on their parameters. Throughout this paper, we use the generic designation "SIG" to refer to any or all of these five signal regions.
The distributions of the number of tagged b jets for the 1BL, 1BT, and 2BT samples (i.e., for the three different sets of selection criteria on H T and E miss T ), except without the requirement on the number of b jets, are shown in Fig. 2  Monte Carlo (MC) simulations of SM processes. Results from the benchmark T1bbbb and T1tttt NP models mentioned in the Introduction are also shown. The simulated tt, W+jets, and Z+jets events are produced at the parton level with the MADGRAPH5.1.1.0 [26] event generator. Single-top-quark events are generated with the POWHEG 301 [27] program. The PYTHIA 6.4.22 program [28] is used to produce diboson and QCD events. For all simulated samples, PYTHIA 6.4 is used to describe parton showering and hadronization. All samples are generated using the CTEQ6 [29] parton distribution functions. The description of the detector response is implemented using the GEANT4 [30] program. The tt sample is normalized to the measured cross section [31]. The other simulated samples are normalized using the most accurate cross section calculations currently available, which is generally NLO. The jet energy resolution in the simulation is corrected to account for a small discrepancy with respect to data [21]. In addition, the simulated samples are reweighted to describe the probability distribution observed in data for overlapping pp collisions within a bunch crossing ("pileup").  As examples illustrating the characteristics of events with at least one, two, or three tagged b  Fig. 3. The numbers of events in the different signal regions are listed in Table 2 for data and simulation. The simulated results are for guidance only and are not used in the analysis. Our method to evaluate the QCD background is based on the ∆φ min variable. This method presumes that most E miss T in a QCD event arises from the p T mismeasurement of a single jet.

The ∆φ min variable
The ∆φ min variable is a modified version of the commonly used quantity ∆φ min ≡ min(∆φ i ) (i = 1, 2, 3), the minimum azimuthal opening angle between the E miss T vector and each of the three highest-p T jets in an event. Misreconstruction of a jet primarily affects the modulus of its transverse momentum but not its direction. Thus QCD background events are characterized by small values of ∆φ min . The ∆φ min variable is strongly correlated with E miss T , as discussed below. This correlation undermines its utility for the evaluation of the QCD background from data. To reduce this correlation, we divide the ∆φ i by their estimated resolutions σ ∆φ,i to obtain ∆φ min ≡ min(∆φ i /σ ∆φ,i ).
The resolution σ ∆φ,i for jet i is evaluated by considering the p T resolution σ p T of the other jets in the event. The uncertainty σ T i on the component of the E miss T vector perpendicular to jet i is found using σ 2 T i ≡ ∑ n (σ p T ,n sin α n ) 2 , where the sum is over all other jets in the event with p T > 30 GeV and α n is the angle between jet n and the direction opposite jet i. The situation is depicted in Fig. 4 for an event with exactly three jets with p T > 30 GeV. Our estimate of the ∆φ resolution is σ ∆φ,i = arctan(σ T i /E miss T ). [Note: arcsin(σ T i /E miss T ) is technically more correct in this expression; we use arctan(σ T i /E miss T ) because it is computationally more robust while being equivalent for the small angles of interest here.] For the jet p T resolution, it suffices to use the simple linear parametrization σ p T = 0.10 p T [21].  The measured results for N(∆φ min ≥ 4.0)/N(∆φ min < 4.0) with zero b jets, for events with H T > 400 GeV, 500 GeV, and 600 GeV, are shown in Fig. 6. By requiring that there not be a b jet, we reduce the contribution of top-quark events, which is helpful for the evaluation of QCD background (Section 5.1). The data in Fig. 6 are collected with a pre-scaled H T trigger, allowing events to be selected at low E miss T without a trigger bias. The data in Fig. 6(a) are seen to somewhat exceed the simulated predictions. The trend is visible in Fig. 6(b) to a lesser extent. This modest discrepancy arises because the ∆φ min distribution is narrower in the simulation than in data. Since our method to evaluate the QCD background is based on the measured distribution, this feature of the simulation does not affect our analysis. The data in Fig. 6 are seen to exhibit the general behavior expected from the simulation. The region below around 100 GeV is seen to be dominated by the QCD background.

Background evaluation
In this section we describe our methods to evaluate the SM background from control samples in data. Each of the three main backgrounds -from QCD, Z+jets, and top-quark and W+jets events (where "top quark" includes both tt and single-top-quark events) -is evaluated separately. We group top quark and W+jets events together because they have a similar experimental signature. Note that our final results for the total SM background are derived from a global likelihood procedure that incorporates our background evaluation procedures into a single fit, and that also accounts for possible NP contributions to the control regions in a consistent manner. The global likelihood procedure is described in Section 6.
QCD background is evaluated using the ∆φ min variable. Background from Z+jets events is evaluated by scaling the measured rates of Z → + − ( = e or µ) events. To estimate the top-quark and W+jet background, we employ two complementary techniques. One, which we call the nominal method, is simple and almost entirely data based, while the other, which we call the E miss T -reweighting method, combines results based on data with information from simulation to examine individual sources of top-quark and W+jets background in detail.

QCD background
The low level of correlation between ∆φ min and E miss T allows us to employ a simple method to evaluate the QCD background from data. As discussed in Section 4, the ratio N(∆φ min ≥ 4.0)/N(∆φ min < 4.0) is approximately independent of E miss T , and also of the number of b jets, for QCD events. Furthermore, the E miss T distribution below 100 GeV is expected to be dominated by QCD events, especially for events with zero b jets (Fig. 6). We therefore measure N(∆φ min ≥ 4.0)/N(∆φ min < 4.0) in a low E miss T region of the zero-b-jet sample and assume this equals N(∆φ min ≥ 4.0)/ N(∆φ min < 4.0) for QCD events at all E miss T values, also for samples with b jets such as our signal samples.
To perform this measurement, we divide the data into sideband and signal regions in the ∆φ min -E miss T plane, as illustrated schematically in Fig. 7. We use the low-E miss T interval defined by 50 < E miss T < 100 GeV and ∆φ min > 4.0. We call this interval the low sideband (LSB) region. We also define low ∆φ min (LDP) intervals ∆φ min < 4.0. We do this not only for the 50 < E miss T < 100 GeV region, but also for the signal regions (SIG) and for a sideband (SB) region defined by 150 < E miss T < 250 GeV. We denote these regions LSB-LDP, SIG-LDP, and SB-LDP, respectively. The LSB-LDP region is dominated by QCD events. Similarly, the SB-LDP and SIG-LDP regions   Table 1. The designation "SIG" generically refers to any of the signal regions in this table. The SIG and SIG-LDP regions shown in the diagram explicitly depict the loose kinematic signal regions 1BL, 2BL, and 3B, which require E miss T > 250 GeV, but implicitly include the tight kinematic signal regions 1BT and 2BT, which require E miss T > 500 GeV and 300 GeV, respectively. For each choice of signal region, the condition on H T specified in Table 1 for that region is applied to all six panels of the diagram, while the condition on the number of b jets is applied to the four panels denoted "Standard selection." All regions with the low ∆φ min (LDP) designation require 0.0 < ∆φ min < 4.0, while the other regions require ∆φ min > 4.0.  T1tttt T1tttt T1tttt Applying corrections for the non-QCD components of the SIG-LDP and SB-LDP regions, our estimates of the QCD yields in the SIG and SB regions are therefore: where the LSB and LSB-LDP results are derived from the zero-b-jet, pre-scaled H T trigger sample mentioned in Section 4. The result for N QCD SB is used in Section 5.3. The ratio N LSB /N LSB−LDP is found to depend on the number of primary vertices (PV) in the event and thus on the LHC instantaneous luminosity. Before evaluating Eqs. (1) and (2), we therefore reweight the events in the pre-scaled sample to have the same PV distribution as the standard sample.
Systematic uncertainties are summarized in Table 3. The systematic uncertainty associated with the subtraction of events with either a top quark or a W or Z boson from the SIG-LDP and SB-LDP regions is determined by varying the subtracted values by their uncertainties, evaluated as described in Section 7. The systematic uncertainty associated with the assumption that E miss T and ∆φ min are uncorrelated is evaluated with an MC closure test, namely by determining the ability of the method to predict the correct yield using simulated samples. We compute (N true − N pred )/N pred , where N pred is the predicted number of QCD events in the signal region, estimated by applying the above procedure to simulated samples treated as data, and N true is the true number. We assign the result, added in quadrature with its statistical uncertainty, as a symmetric systematic uncertainty. This uncertainty is dominated by statistical uncertainties for N true . The closure test is performed both for the standard simulated samples and for simulated samples that are reweighted to account for discrepancies in the jet multiplicity distributions between data and simulation; we take the larger closure discrepancy as the uncertainty. A third systematic uncertainty is evaluated by taking ±100% of the shift in the result caused by the PV reweighting of N LSB /N LSB−LDP . The systematic uncertainty associated with the trigger efficiency is found to be negligible.
As a cross-check, we vary the definition of the LSB by raising and lowering its lower edge by 10 GeV, which alters the number of events in the LSB by more than a factor of two in each case. The observed change in the QCD background estimate is negligible.

Z+jets background
Events with a Z boson and one or more b jets present an irreducible background when the Z decays to two neutrinos. We evaluate this background by reconstructing Z → + − events ( = e or µ) and removing the + and − . Fits are performed to determine the Z → + − yields, which are then corrected for background and efficiency. The efficiency is = A · trig · 2 reco · 2 sel , where the geometrical acceptance A is determined from simulation while the trigger trig , lepton reconstruction reco , and lepton selection sel efficiencies are determined from data. The corrected Z → + − yields are used to estimate the Z → νν background through scaling by the ratio of branching fractions, BR (Z → νν)/BR (Z → + − ) = 5.95 ± 0.02 [32], after accounting for the larger acceptance of Z → νν events.
The Z → + − yields are small or zero in the signal regions. To increase these yields, we select events with the signal-sample requirements except with a significantly looser b-tagging definition. A scale factor derived from a control sample in data is then applied to estimate the number of Z → + − events in the signal regions. The control sample is defined with the same loosened b-tagging definition, but without requiring the presence of a Z boson, and also by reversing the ∆φ min requirement, i.e., we require ∆φ min < 4.0, which yields a control sample with a b-jet content similar to that in the Z → + − and Z → νν events. All other selection criteria are the same as for the corresponding signal sample. The scale factors are given by the fraction of events in the control sample that passes the nominal b-tagging requirements. The scale factors have values around 0.30, 0.07, and 0.01 for the samples with ≥ 1, ≥ 2, and ≥ 3 b jets, respectively. We verify that the output of the b-tagging algorithm is independent of the presence of a Z.
We validate our method with a consistency test, applying the above procedure to data samples with loosened restrictions on H T and E miss T . We find the number of predicted and observed Z → + − events to be in close agreement.
Systematic uncertainties are summarized in Table 4. We evaluate a systematic uncertainty on the scale factors by loosening and tightening the b-tagging criterion of the control sample and taking half the difference between the two results as an uncertainty. The size of the control sample changes by about ±30% in these variations. In addition, we use ∆φ min > 4.0 rather  (30) 52 (65) 52 (65) 150 (110) than ∆φ min < 4.0 to define the control sample and calculate the difference with respect to the nominal results. Finally, we evaluate the percentage difference between the number of predicted and observed events found with the consistency test described above. The three terms are added in quadrature to define the systematic uncertainty of the scale factors. We evaluate a systematic uncertainty associated with the non-resonant + − background to Z → + − events by comparing the fraction of fitted events in the Z → + − peak from the nominal fit with those found using either a loosened H T or a loosened E miss T restriction. The RMS of the three results is added in quadrature with the statistical uncertainty from the nominal fit to define the systematic uncertainty. The 1BL selection is used to determine this uncertainty for all signal regions. A systematic uncertainty for the acceptance is defined by recalculating the acceptance after varying the p T and η ranges of the + and − . The largest difference with respect to the nominal result is added in quadrature with the statistical uncertainty of the acceptance. A systematic uncertainty is defined for the lepton selection efficiency, and analogously for the trigger efficiency, by recalculating the respective efficiency after varying the requirements on H T , E miss T , ∆φ min , the number of jets, and the number of b jets (the number of jets is found using all jets with p T > 50 GeV and |η| < 2.4). We also use alternative signal and background shapes in the fits used to extract the Z → + − event yields. The maximum variations from each case are added in quadrature with the statistical uncertainty from the nominal method to define the systematic uncertainties. Finally, we evaluate a systematic uncertainty based on an MC closure test in the manner described in Section 5.1. We use the SB region to determine this uncertainty.
An analogous procedure to that described above is used to evaluate the number of Z → νν events N Z→νν SB in the SB regions (150 < E miss T < 250 GeV), along with the corresponding uncertainty.

Top-quark and W+jets background (nominal)
For most signal regions, tt events are expected to be the dominant background (Table 2). Backgrounds from single-top-quark and W+jets events are expected to be smaller but to have a similar signature. Almost all top-quark and W+jets background in our analysis arises either because a W boson decays leptonically to an e or a µ, with the e or µ unidentified, not isolated, or outside the acceptance of the analysis, or because a W boson decays to a hadronically decaying τ lepton. We find empirically, through studies with simulation, that the shape of the E miss T distribution is similar for all top-quark and W+jets background categories that enter the signal (Table 1) or sideband (150 < E miss T < 250 GeV) regions, regardless of whether the W boson decays to e, µ, or τ, or whether a τ lepton decays hadronically or leptonically: the decay of the W boson in W+jets events generates an E miss T spectrum (from the neutrino) that is similar to the E miss T spectrum generated by the W boson produced directly in the decay of a top quark in top quark events. Additional, softer neutrinos in events with a τ lepton do not much alter this spectrum. We also find that this shape is well-modeled by the E miss T distribution of a singlelepton (SL) control sample formed by inverting the lepton veto, i.e., by requiring that exactly one e or one µ be present using the lepton identification criteria of Section 3, in a sample whose selection is otherwise the same as the corresponding signal sample, except to reduce the potential contribution of NP to the SL samples, we impose an additional restriction M T < 100 GeV on the SL samples (only), where M T is the transverse W-boson mass formed from the charged lepton and E miss T momentum vectors. As an illustration, Fig. 9 shows a comparison based on simulation of the E miss T distributions in the signal and SL samples, for events selected with the 1BL, 2BT, and 3B criteria.
The E miss T distributions of events in the SL samples with the 1BL, 2BT, and 3B requirements are shown in Fig. 10. The distributions are seen to be overwhelmingly composed of tt events (for example, according to simulation, top and W+jets events comprise over 98% of the events in the SB-SL samples for all SIG selections). The expected contributions of the benchmark T1bbbb NP scenario are found to be negligible, while those of the benchmark T1tttt scenario are seen to be small in Fig. 10   Based on these observations, we implement a template method in which the shape of the E miss T distribution in an SL sample is used to describe the shape of the E miss T distribution in the corresponding signal sample of  Fig. 11. Contributions to the SB region from QCD and Z → νν events are taken from the data-based estimates of Sections 5.1 and 5.2. Small, residual contributions from other backgrounds such as diboson events are subtracted using simulation.   Fig. 7. The sideband-single-lepton (SB-SL) and signal-single-lepton (SIG-SL) regions correspond to the SB and SIG regions, respectively, except an electron or muon is required to be present and a requirement is placed on the transverse W boson mass M T < 100 GeV. Our estimate of the top-quark and W+jets background in the SIG region is therefore: Contamination of the SB region in the benchmark T1bbbb (T1tttt) NP scenario is predicted to be around 1% (1%) for the 1BL, 1BT, and 2BL selections, 4% (3%) for the 2BT selection, and 7% (5%) for the 3B selection. The likelihood procedure described in Section 6 accounts for NP contributions to all control regions in a coherent manner.
Systematic uncertainties are summarized in Table 5. We consider the systematic uncertainty associated with MC closure, evaluated as described in Section 5.1. The closure is evaluated separately for the nominal combined top-quark and W+jets simulated sample, with the W+jets cross section increased by 50% and the single-top-quark cross section by 100%, and with the W+jets cross section decreased by 50% and the single-top-quark cross section by 100% (these variations account for uncertainties on the relative cross sections; they are based on the uncertainties of the NLO calculations and on comparisons between data and simulation). We take the largest closure discrepancy as the uncertainty. We also consider the systematic uncertainty associated with subtraction of the QCD-and Z → νν-background estimates in the SB region, evaluated by varying these estimates by their uncertainties. The systematic uncertainty associated with other backgrounds is evaluated by varying the MC-based background estimates in the SB region by their uncertainties, which we assume to be ±100% for these small terms. A final systematic uncertainty accounts for the uncertainty on the trigger efficiency.

T -reweighting)
We perform a second, complementary evaluation of the top-quark and W+jets background, which we refer to as the E miss T -reweighting method. The E miss T distribution is determined separately for each of the three principal top-quark and W+jets background categories: 1. top-quark or W+jets events in which exactly one W boson decays into an e or µ, or into a τ that decays into an e or µ, while the other W boson (if any) decays hadronically; 2. top-quark or W+jets events in which exactly one W boson decays into a hadronically decaying τ, while the other W boson (if any) decays hadronically; 3. tt events in which both W bosons decay into an e, µ or τ, with the τ decaying either leptonically or hadronically.
For the 1BL selection, these three categories represent, respectively, approximately 44%, 49%, and 7% of the total expected background from top-quark and W+jets events, as determined from simulation.

Top-quark and W+jets background (E miss
T -reweighting) 15

Single e or µ events: category 1
Category 1 top-quark and W+jets background is evaluated with the SL data control sample introduced in Section 5.3. To relate event yields in the SL and SIG samples, we use constraints derived from knowledge of the W-boson polarization. The polarization of the W boson governs the angular distribution of leptons in the W boson rest frame. Because forward-going leptons are boosted to higher momentum, and backward-going leptons to lower momentum, the W-boson polarization is directly related to the lepton momentum spectrum in the laboratory frame. W-boson polarization is predicted to high precision in the SM, with calculations carried out to the next-to-next-to-leading order for tt events [33] and to NLO for W+jets events [34].
To construct a distribution sensitive to the W-boson polarization in W → ν ( = e, µ) events (we include W → τν → ννν events in this category), we calculate the angle ∆θ T between the direction of the W boson in the laboratory frame and the direction of the e or µ in the W boson rest frame, all defined in the transverse plane. The p T of the W boson is given by the vector sum of the E miss T and charged lepton p T vectors. When ∆θ T is small, the charged lepton is produced along the p T direction of the W boson, typically resulting in a high-p T charged lepton and a low-p T neutrino (and therefore low E miss T ) in the laboratory frame. Such events usually appear in the SL sample. Conversely, when ∆θ T is large, the charged lepton (neutrino) has lower (higher) p T , typically leading to larger E miss T , a charged lepton that fails our e or µ identification criteria, and an event that appears as background in the signal samples.  Figure 12 shows the distribution of ∆θ T in data and simulation for SL events selected with the 1BL, 2BT, and 3B criteria, except a looser E miss T requirement (E miss T > 250 GeV) is used for the 2BT region to reduce statistical fluctuations. These results can be compared to those expected in the limit of perfect charged lepton reconstruction, indicated by the dashed histograms in Fig. 12, which show the corresponding simulated predictions, including simulation of the detector, for top-quark and W+jets events with a single W → ν decay, where the e or µ needs only to be present at the generator level. The difference between the dashed histogram and the sum of the histograms with exactly one true e or µ found in the event represents W → ν events in which the e or µ is either not reconstructed or does not meet the selection criteria of Section 3.
To estimate the E miss T distribution of category 1 events, we measure the E miss T distribution of SL events in bins of ∆θ T . The E miss T distribution for each bin is then multiplied by an MC

1BL
1BT scale factor, determined as follows. The numerator equals the difference between the total yield from single-lepton processes (the dashed histograms in Fig. 12) and the subset of those events that enter the SL sample, both determined for that bin. The denominator equals the corresponding number of events that appear in the SL sample from all sources. The definition of the denominator therefore corresponds to the SL observable in data. The normalization of the E miss T distribution in each ∆θ T bin is thus given by the corresponding measured yield, corrected by a scale factor that accounts for the e or µ acceptance and reconstruction efficiency. The corrected E miss T spectra from the different ∆θ T bins are summed to provide the total E miss T distribution for category 1 events.
Systematic uncertainties are summarized in Table 6. To evaluate a systematic uncertainty associated with the relative tt and W+jets cross sections, we vary the W+jets cross section by ±50%. From studies of Z → + − events, the systematic uncertainty associated with the lepton reconstruction efficiency is determined to be 2%. A systematic uncertainty associated with the top-quark p T spectrum is evaluated by varying the W-boson p T distribution in the simulated tt sample. In these variations, the number of events in the upper 10% of the distribution changes by two standard deviations of the corresponding result in data. The systematic uncertainties associated with the jet energy scale, jet energy resolution, and b-tagging efficiency are evaluated as described in Section 7. A systematic uncertainty to account for MC closure is evaluated as described in Section 5.3.

τ → hadrons: category 2
Category 2 top-quark and W+jets background is evaluated using a single-muon data control sample. The muon in the event is replaced with a simulated hadronically decaying τ (a τ jet) of the same momentum. To account for the addition of the τ jet, the initial selection criteria are less restrictive than those of the nominal analysis. We require two or more jets, E miss T > 100 GeV, and do not place restrictions on H T or ∆φ min . To ensure compatibility with the triggers used to define this single-muon control sample, the minimum muon p T is set to 25 GeV, and the muon isolation requirement is also more stringent than the nominal criterion of Section 3.
The visible energy fraction of the τ jet, namely its visible energy divided by its p T value, is determined by sampling p T -dependent MC distributions ("response templates") of the τ visible energy distribution, for a given underlying value of τ lepton p T . The τ jet visible energy is added to the event. The modified event is then subjected to our standard signal region selection criteria. A normalization factor derived from simulation accounts for the relative rates of category 2 and single-muon control sample events. Table 7: The SM background estimates from the procedures of Sections 5. 1-5.4 in comparison with the observed number of events in data. The first uncertainties are statistical and the second systematic. For the total SM estimates, we give the results based both on the nominal and E miss T reweighting methods to evaluate the top-quark and W+jets background.

tt dilepton events: category 3
The contribution of category 3 top-quark and W+jets background events is determined using dilepton data control samples. When both leptons are electrons or both are muons, or when one is an electron and the other a muon (where the e or µ can either be from a W boson or τ decay), we use simulated predictions to describe the shape of the E miss T distribution. The normalization is derived from data, by measuring the number of dilepton events that satisfy loosened selection criteria for each class of events (ee, µµ, or eµ) individually. The measured value is multiplied by an MC scale factor, defined by the number of corresponding tt dilepton events that satisfy the final selection criteria divided by the number that satisfy the loosened criteria.
When one or both of the leptons is a hadronically decaying τ, we apply a procedure similar to that described for category 2 events. Data control samples of eµ+jets and µµ+jets events are selected with the loosened criteria of Section 5.4.2. One or both muons is replaced by a τ-jet using MC response templates. The signal sample selection criteria are applied to the modified events, and the resulting E miss T distributions normalized by scaling the number of events in the respective control samples with factors derived from MC simulation.
The E miss T distributions of all six dilepton categories are summed to provide the total category 3 prediction. A systematic uncertainty is evaluated based on MC closure in the manner described in Section 5.1.

Summary of the data-based background estimates
A summary of the background estimates is given in Table 7. The results from the three categories of Section 5.4 are summed to provide the total E miss T -reweighting top-quark and W+jets prediction. The estimates from the E miss T -reweighting method are seen to be consistent with those from the nominal method and to yield smaller uncertainties. Note that there are statistical correlations between the nominal and E miss T -reweighting methods because they both make use of the SIG-SL region of Fig. 11. However, the nominal method relies on the SB and SB-SL regions of Fig. 11, while the E miss T -reweighting method does not. The E miss T -reweighting method makes use of MC scale factors and data selected with lepton-based triggers (for category 2 and 3 events), while the nominal method does not. Furthermore, the systematic uncertainties of the two methods are largely uncorrelated (compare Tables 5 and 6).
The data are generally in good agreement with the SM expectations. However, for 2BT, the data lie 1.1 and 2.2 standard deviations (σ) above the predictions (including systematic uncertainties) for the nominal and E miss T -reweighting methods, respectively. For 3B, the corresponding deviations are 1.2σ and 0.7σ. Since these deviations are not significant, we do not consider them further.
As an illustration, Fig. 13 presents the background predictions in comparison to data for the 1BL, 2BT, and 3B selections. These results are based on the nominal top-quark and W+jets background estimate. We perform a global likelihood fit that simultaneously determines the SM background and yield of a NP model, using the background estimation techniques of Section 5. The likelihood analysis allows us to treat the SM backgrounds in a more unified manner than is possible through the collection of individual results in Table 7. Furthermore, it allows us to account for NP contributions to the control regions ("signal contamination"), as well as to the signal region, in a comprehensive and consistent manner.

Likelihood analysis
It is difficult to account for signal contamination using the E miss T -reweighting method, in contrast to the nominal method. Therefore, signal contamination is evaluated for the nominal method only. Of the two NP scenarios we consider, one of them, the T1tttt model, exhibits non-negligible contamination of the SL samples, while the other, the T1bbbb model, does not. Since the T1bbbb model does not exhibit significant signal contamination, we employ both the nominal-and E miss T -reweighting-based likelihood fits for this model. For the T1tttt model, we employ only the likelihood fit based on the nominal method.
For the nominal method, the data are divided into 11 mutually exclusive bins, corresponding to the 11 observables listed in Table 8, where each "observable" corresponds to the number of data events recorded for that bin. Note that the SB-SL events of Fig. 11 are divided into two components, one for electrons (denoted SB-Se) and the other for muons (denoted SB-Sµ), because their trigger efficiencies and uncertainties differ. Similarly, the reconstruction efficiencies . The four Z → + − samples are denoted SIG-ee and SIG-µµ for events in the signal regions, and SB-ee and SB-µµ for events in the sideband region.
The likelihood model provides a prediction for the mean expected value of each observable in terms of the parameters of the signal and background components. The likelihood function is the product of 11 Poisson probability density functions, one for each observable, β distributions [40] that parametrize efficiencies and acceptances, and β distributions [40] that account for systematic uncertainties and uncertainties on external parameters. (External parameters include such quantities as the acceptance A and scale factors between the samples with loose and nominal b-tagging requirements discussed in Section 5.2.) The new physics scenarios considered here can contribute significantly to the seven observables listed in the upper portion of Table 8. In our model, the relative contributions of NP to these seven observables are taken from the NP model under consideration. The NP yield in the SIG bin is a free parameter. The NP contributions to the other six bins thus depend on the NP yield in the SIG bin.
Analogous procedures are used to define the likelihood function for the E miss T -reweighting method, with simplifications since there is no SB region in this case.
The likelihood function is used to set limits on NP models. Upper limits at 95% confidence level (CL) are evaluated taking into account the effects of variation of the external parameters and their correlations. All upper limits are determined using a modified frequentist technique (CL s ) [41,42].

Limits on the T1bbbb and T1tttt models
Simulated T1bbbb and T1tttt event samples are generated for a range of gluino and LSP masses using PYTHIA, with m LSP < m g . For increased efficiency when performing scans over the SMS parameter space (see below), we base simulation of the CMS detector response on the fast simulation program [43], accounting for modest differences observed with respect to the GEANT4 simulation. Systematic uncertainties on signal efficiency are summarized in Table 9, using the T1bbbb benchmark model as an example. A systematic uncertainty associated with the jet energy scale is evaluated by varying this scale by its p T -and η-dependent uncertainties. A systematic uncertainty associated with unclustered energy is evaluated by varying the transverse energy in an event that is not clustered into a physics object by ±10%. The systematic uncertainties associated with the correction to the jet energy resolution, the pileup reweighting method mentioned in Section 3, the b-jet tagging efficiency scale factor, and the trigger efficiency, are evaluated by varying the respective quantities by their uncertainties. The uncertainty for the trigger efficiency includes a 2.5% uncertainty for the plateau efficiency. Systematic uncertainties associated with the parton distribution functions are evaluated following the recommendations of Ref. [44]. The systematic uncertainty associated with anomalous E miss T values, caused by beam background and reconstruction effects, is 1%. The systematic uncertainty associated with the lepton veto is determined from studies of Z → + − events in data to be 3.0%. The uncertainty in the luminosity determination is 2.2% [45].
We determine 95% CL upper limits on the SMS cross sections as a function of the gluino and LSP masses. Using the NLO+NLL cross section as a reference, we also evaluate 95% CL exclusion curves. The jet energy scale, unclustered energy, parton distribution function, and b-jet tagging efficiency uncertainties are evaluated for each scan point. Other uncertainties are fixed to the values in Table 9. For each choice of gluino and LSP mass, we use the combination of the top-quark and W+jets background estimation method, and the signal selection (Table 1), that provides the best expected limit. We do not include results for points near the m g = m LSP diagonal because of neglected uncertainties from initial-state radiation (ISR), which are large in this region. Specifically, we remove from consideration any point for which the signal efficiency changes by more than 50% when the ISR radiation in PYTHIA is (effectively) turned off. For the T1bbbb model, the E miss T -reweighting method is always found to provide the best expected result: we therefore use this method to determine the T1bbbb limits. The E miss T reweighting method incorporates an additional constraint compared to the nominal method, namely the normalization of the SM prediction for the E miss T distribution from the SIG-SL sample (Fig. 11), and not merely the E miss T distribution shape. As a consequence, it has greater discrimination power against NP scenarios.
The results for T1bbbb are shown in Fig. 14(a). The 1BT selection is found to provide the best expected result in the bottom right corner of the distribution, corresponding to the region of large gluino-LSP mass splitting. The 2BT selection is best for the swath roughly parallel to the  Figure 15: (a) The 95% CL observed cross section upper limits (UL) for the T1tttt SMS model, based on the nominal method to evaluate the top-quark and W+jets background. For each point, the selection that provides the best expected cross section limit is used (the best selection is virtually always 3B). The solid contour shows the 95% CL exclusion limits on the gluino and LSP masses using the NLO+NLL cross section for new physics. The dashed contours represent the theory uncertainties. (b) The corresponding expected limits. The dashed contours represent the uncertainties on the SM background estimates. diagonal defined by gluino masses between around 650 and 900 GeV along the bottom edge of the plot. The 3B selection is generally best elsewhere. The solid contour shows the 95% CL exclusion curve for the reference cross section. The zigzagging structure around m g = 900 GeV, m LSP = 450 GeV is due to the transition from the region where 3B is the best expected selection to that where 2BT is best, in conjunction with the slight excess observed in data for the 2BT selection in comparison with the SM prediction for the E miss T -reweighting method (Section 5.5). The dashed contours represent the results when the reference cross section is varied by the theory uncertainty [46]. Our results improve those of Ref. [7] for large LSP mass values. For example, for gluino masses around 800 GeV, we extend the exclusion of the reference cross section from an LSP mass of about 400 GeV [7] to about 500 GeV, where these numerical values are given by the observed results minus the one standard deviation theory uncertainties. Fig. 14(b) shows the best expected results for the T1bbbb model. In this case the dashed contours represent the results when the SM background estimates (Table 7) are varied by their uncertainties.
Even with the selection requirement against ISR events described above, the effect of ISR events can be significant for T1bbbb scenarios that lie within three or four cell widths of the diagonal, where the size of a cell is indicated by the small boxes visible near the diagonal in Fig. 14. We do not account for the effect of ISR for these scenarios. However, for gluino masses less than around 500 GeV, and for points more than three to four cell widths from the diagonal, the effect of ISR is negligible for the points that are retained. This includes the entire exclusion region for the NLO+NLL reference cross section.
The corresponding results for the T1tttt model are presented in Fig. 15. Our T1tttt results are based on the nominal top-quark and W+jets background estimation method for the reason stated in Section 6. In this case, the best expected selection is essentially always 3B. Note that the observed limits for T1tttt, shown in Fig 15(a), are not as stringent as the expected limits, shown in Fig 15(b), because of the slight excess of data events in the 3B sample for the nominal method, compared to the SM expectation (Table 7).

Summary
In this paper, we present a search for an anomalous rate of events with three or more jets, at least one, two, or three tagged bottom-quark jets, no identified, isolated leptons, and large missing transverse energy E miss T . The study is based on a sample of proton-proton collision data collected at √ s = 7 TeV with the CMS detector at the LHC during 2011, corresponding to an integrated luminosity of 4.98 fb −1 . The principal standard model backgrounds, arising from top-quark, W+jets, Z+jets, and QCD-multijet events, are evaluated from data. We introduce a variable ∆φ min that allows us to address the QCD-multijet background with a simple approach. The top-quark and W+jets background is evaluated with two complementary methods, which yield consistent results. In the E miss T -reweighting method to evaluate the top-quark and W+jets background, we introduce a technique based on the W polarization in tt and W+jets events. Our analysis is performed in a likelihood framework in order to account for backgrounds, and for new physics contamination of the control regions, in a unified and consistent manner.
We find no evidence for a significant excess of events beyond the expectations of the standard model and set limits on new physics in the context of the b-jet-rich T1bbbb and T1tttt simplified model spectra, in which new strongly interacting particles decay to two b-quark jets, or two tquark jets, plus an undetected particle. For the T1bbbb scenario, our results improve on those of Ref. [7] for large LSP masses.