Search for supersymmetry in multijet events with missing transverse momentum in proton-proton collisions at 13 TeV

: A search for supersymmetry is presented based on multijet events with large missing transverse momentum produced in proton-proton collisions at a center-of-mass energy of √ s =13 TeV. The data, corresponding to an integrated luminosity of 35.9 fb 1 , were collected with the CMS detector at the CERN LHC in 2016. The analysis utilizes four-dimensional exclusive search regions defined in terms of the number of jets, the number of tagged bottom quark jets, the scalar sum of jet transverse momenta, and the magnitude of the vector sum of jet transverse momenta. No evidence for a significant excess of events is observed relative to the expectation from the standard model. Limits on the cross sections for the pair production of gluinos and squarks are derived in the context of simplified models. Assuming the lightest supersymmetric particle to be a weakly interacting neutralino, 95% confidence level lower limits on the gluino mass as large as 1800 to 1960 GeV are derived, and on the squark mass as large as 960 to 1390 GeV, depending on the production and decay scenario. A search for supersymmetry is presented based on multijet events with large missing transverse momentum produced in proton-proton collisions at a center-of-mass energy of ﬃﬃﬃ s p ¼ 13 TeV. The data, corresponding to an integrated luminosity of 35 . 9 fb − 1 , were collected with the CMS detector at the CERN LHC in 2016. The analysis utilizes four-dimensional exclusive search regions defined in terms of the number of jets, the number of tagged bottom quark jets, the scalar sum of jet transverse momenta, and the magnitude of the vector sum of jet transverse momenta. No evidence for a significant excess of events is observed relative to the expectation from the standard model. Limits on the cross sections for the pair production of gluinos and squarks are derived in the context of simplified models. Assuming the lightest supersymmetric particle to be a weakly interacting neutralino, 95% confidence level lower limits on the gluino mass as large as 1800 to 1960 GeVare derived, and on the squark mass as large as 960 to 1390 GeV, depending on the production and decay scenario.


I. INTRODUCTION
The standard model (SM) of particle physics describes many aspects of weak, electromagnetic, and strong interactions. However, it requires fine-tuning [1] to explain the observed value of the Higgs boson mass [2], and it does not provide an explanation for dark matter. Supersymmetry (SUSY) [3][4][5][6][7][8][9][10], a widely studied extension of the SM, potentially solves these problems through the introduction of a new particle, called a superpartner, for each SM particle, with a spin that differs from that of its SM counterpart by a half unit. Additional Higgs bosons and their superpartners are also introduced. The superpartners of quarks and gluons are squarksq and gluinosg, respectively, while neutralinosχ 0 and charginosχ AE are mixtures of the superpartners of the Higgs and electroweak gauge bosons. Provided that the masses of gluinos, top squarks, and bottom squarks are no heavier than a few TeV, SUSY can resolve the fine-tuning problem [1,[11][12][13]. Furthermore, in R-parity [14] conserving SUSY models, the lightest SUSY particle (LSP) is stable and might interact only weakly, thus representing a dark matter candidate.
In this paper, we present a search for squarks and gluinos produced in proton-proton (pp) collisions at ffiffi ffi s p ¼ 13 TeV. Squark and gluino production have large potential cross sections in pp collisions, thus motivating this search. The study is performed in the multijet final state, i.e., the visible elements consist solely of jets. Other ffiffi ffi s p ¼ 13 TeV inclusive multijet SUSY searches were presented in Refs. [15][16][17][18][19][20]. We assume the conservation of R parity, meaning that the squarks and gluinos are produced in pairs. The events are characterized by the presence of jets and undetected, or "missing," transverse momentum, where the missing transverse momentum arises from the weakly interacting and unobserved LSPs. The data, corresponding to an integrated luminosity of 35.9 fb −1 , were collected in 2016 with the CMS detector at the CERN LHC. The analysis is performed in four-dimensional exclusive regions in the number of jets N jet , the number of tagged bottom quark jets N b-jet , the scalar sum H T of the transverse momenta p T of jets, and the magnitude H miss T of the vector p T sum of jets. The number of observed events in each region is compared with the expected number of SM events to search for excesses in the data.
The study is an extension of that presented in Ref.
[17], using improved analysis techniques and around 16 times more data. Relative to Ref. [17], the following principal modifications have been made. First, the search intervals in N jet and H T are given by N jet ≥ 2 and H T > 300 GeV, compared with N jet ≥ 4 and H T > 500 GeV in Ref. [17]. Inclusion of events with N jet ¼ 2 and 3 increases the sensitivity to squark pair production. The lower threshold in H T provides better sensitivity to scenarios with small mass differences between the LSP and the squark or gluino. Second, the rebalance-and-smear technique [21,22] is introduced as a complementary means to evaluate the quantum chromodynamics (QCD) background, namely the background from SM events with multijet final states produced exclusively through the strong interaction. Third, the search interval in H miss T is given by H miss T > 300 GeV, rather than the previous H miss T > 200 GeV, in order to reserve the QCD-dominated 250 < H miss T < 300 GeV region for a QCD background control sample in data. A final principal change is that finer segmentation than in Ref. [17] is used to define exclusive intervals in H T and H miss T , to profit from the increased sensitivity afforded by the larger data sample.
Supersymmetric particles not participating in the respective reaction are assumed to have infinite mass. All considered SUSY particles are taken to decay promptly.
Background from SM processes arises from events with a top quark (either tt events or events with a single top quark), events with jets and an on-or off-shell W or Z boson (W þ jets and Z þ jets events, respectively), and QCD events. Top quark and W þ jets events can exhibit significant H miss T and thus contribute to the background if a W boson decays to a neutrino and an undetected or out-ofacceptance charged lepton. Similarly, Z þ jets events can exhibit significant H miss T if the Z boson decays to two neutrinos. Significant H miss T in QCD events is mostly the consequence of mismeasured jet p T , but it can also arise if an event contains a charm or bottom quark that decays semileptonically. Note that tt events in which both top quarks decay hadronically are indistinguishable in our analysis from QCD events and are accounted for in the evaluation of the QCD background. Because the cross section is small compared to that for QCD events, allhadronic tt events comprise only a small (subpercent level) component of the evaluated QCD background.

II. DETECTOR AND TRIGGER
A detailed description of the CMS detector, along with a definition of the coordinate system and pertinent kinematic variables, was given in Ref. [28]. Briefly, a cylindrical superconducting solenoid with an inner diameter of 6 m provides a 3.8 T axial magnetic field. Within the cylindrical volume are a silicon pixel and strip tracker, a lead tungstate crystal electromagnetic calorimeter (ECAL), and a brass and scintillator hadron calorimeter (HCAL). The tracking detectors cover the pseudorapidity range jηj < 2.5. The ECAL and HCAL, each composed of a barrel and two endcap sections, cover jηj < 3.0. Forward calorimeters extend the coverage to 3.0 < jηj < 5.0. Muons are measured within jηj < 2.4 by gas-ionization detectors embedded in the steel flux-return yoke outside the solenoid. The detector is nearly hermetic, permitting accurate measurements of H miss T . The CMS trigger was described in Ref. [29]. For this analysis, signal event candidates were recorded by requiring H miss T at the trigger level to exceed a threshold that varied between 100 and 120 GeV depending on the LHC instantaneous luminosity. The efficiency of this trigger, which exceeds 98% following application of the event selection criteria described below, is measured in data and is taken into account in the analysis. Additional triggers, requiring the presence of charged leptons, photons, or minimum values of H T , are used to select samples employed in the evaluation of backgrounds, as described below.

III. EVENT RECONSTRUCTION
Individual particles are reconstructed with the CMS particle-flow (PF) algorithm [30], which identifies them as photons, charged hadrons, neutral hadrons, electrons, or muons. To improve the quality of electron candidates [31], additional criteria are imposed on the ECAL shower shape and on the ratio of associated energies in the HCAL and ECAL. Analogously, for muon candidates [32], more stringent requirements are imposed on the matching between silicon-tracker and muon-detector track segments. Electron and muon candidates are restricted to jηj < 2.5 and < 2.4, respectively.
The reconstructed vertex with the largest value of summed physics-object p 2 T is taken to be the primary pp interaction vertex. The physics objects are the objects returned by a jet finding algorithm [33,34] applied to all charged tracks associated with the vertex, plus the corresponding associated missing transverse momentum. The primary vertex is required to lie within 24 cm of the center of the detector in the direction along the beam axis and within 2 cm in the plane transverse to that axis. Chargedparticle tracks associated with vertices other than the primary vertex are removed.
To suppress jets erroneously identified as leptons and genuine leptons from hadron decays, electron and muon candidates are subjected to an isolation requirement. The isolation criterion is based on the variable I, which is the scalar p T sum of charged hadron, neutral hadron, and photon PF candidates within a cone of radius ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi ðΔϕÞ 2 þ ðΔηÞ 2 p around the lepton direction, divided by the lepton p T , where ϕ is the azimuthal angle. The expected contributions of neutral particles from extraneous pp interactions (pileup) are subtracted [35]. The radius of the cone is 0.2 for lepton p T < 50 GeV, 10 GeV=p T for 50 ≤ p T ≤ 200 GeV, and 0.05 for p T > 200 GeV. The decrease in cone size with increasing lepton p T accounts for the increased collimation of the decay products from the lepton's parent particle as the Lorentz boost of the parent particle increases [36]. The isolation requirement is I < 0.1 (0.2) for electrons (muons).
Charged-particle tracks not identified as an isolated electron or muon, including PF electrons and muons not so identified, are subjected to a track isolation requirement. To be identified as an isolated track, the scalar p T sum of all other charged-particle tracks within a cone of radius 0.3 around the track direction, divided by the track p T , must be less than 0.2 if the track is identified as a PF electron or muon and less than 0.1 otherwise. Isolated tracks are required to satisfy jηj < 2.4.
Jets are defined by clustering PF candidates using the anti-k T jet algorithm [33,34] with a distance parameter of 0.4. Jet quality criteria [37] are imposed to eliminate jets from spurious sources such as electronics noise. The jet energies are corrected for the nonlinear response of the detector [38] and to account for the expected contributions of neutral particles from pileup [35]. Jets are required to have p T > 30 GeV.
The identification of bottom quark jets (b jets) is performed by applying the combined secondary vertex algorithm (CSVv2) at the medium working point [39] to the selected jet sample. The signal efficiency for b jets with p T ≈ 30 GeV is 55%. The corresponding misidentification probability for gluon and light-flavored (charm) quark jets is 1.6 (12)%.

IV. EVENT SELECTION AND SEARCH REGIONS
Events considered as signal candidates are required to satisfy the following criteria: (1) N jet ≥ 2, where jets must appear within jηj < 2.4.
(2) H T > 300 GeV, where H T is the scalar p T sum of jets with jηj < 2.4.
T , the negative of the vector p T sum of jets with jηj < 5; an extended η range is used to calculate H miss T so that it better represents the total missing transverse momentum in an event. (4) No identified, isolated electron or muon candidate with p T > 10 GeV. (5) No isolated track with m T < 100 GeV and p T > 10 GeV (p T > 5 GeV if the track is identified as a PF electron or muon), where m T is the transverse mass [40] formed from the ⃗p miss T and isolated-track p T vector, where ⃗p miss T is the negative of the vector p T sum of all PF objects. (6) Δϕ H miss T ;j i > 0.5 for the two highest p T jets j 1 and j 2 , where Δϕ H miss T ;j i is the azimuthal angle between ⃗ H miss T and the p T vector of jet j i ; if N jet ≥ 3, then, in addition, Δϕ H miss T ;j 3 > 0.3 for the third highest p T jet j 3 ; if N jet ≥ 4, then, yet in addition, Δϕ H miss T ;j 4 > 0.3 for the fourth highest p T jet j 4 ; all considered jets must have jηj < 2.4. In addition, anomalous events with reconstruction failures or that arise from noise or beam halo interactions are removed [41]. A breakdown of the efficiency at different stages of the selection process for representative signal models is given in Tables IV and V of Appendix A.
The isolated-track veto requirement suppresses events with a hadronically decaying τ lepton, or with an isolated electron or muon not identified as such; the m T requirement restricts the isolated-track veto to situations consistent with W boson decay. The selection criteria on Δϕ H miss T ;j i suppress background from QCD events, for which ⃗ H miss T is usually aligned along a jet direction.
The search is performed in four-dimensional exclusive regions of N jet , N b-jet , H T , and H miss T . The search intervals in N jet and N b-jet are (1) N jet : 2, 3-4, 5-6, 7-8, ≥ 9; (2) N b-jet : 0, 1, 2, ≥ 3. Intervals with N b-jet ≥ 3 and N jet ¼ 2 are discarded since there are no entries. For H T and H miss T , ten kinematic intervals are defined, as specified in Table I Fig. 2) because such events are likely to arise from mismeasurement. For N jet ≥ 7, the kinematic intervals labeled 1 and 4 are discarded because of the small number of events. The total number of search regions is 174.
The intervals labeled C1, C2, and C3 in Fig. 2 are control regions defined by 250 < H miss T < 300 GeV, with the same boundaries in H T as kinematic intervals 1, 2, and 3, respectively. These regions are used in the method to estimate the QCD background described in Sec. VII C 2.

V. SIMULATED EVENT SAMPLES
To evaluate the background, we mostly rely on data control regions, as discussed in Sec. VII. Samples of simulated SM events are used to validate the analysis procedures and for some secondary aspects of the background estimation. The SM production of tt, W þ jets, Z þ jets, γ þ jets, and QCD events is simulated using the MADGRAPH5_AMC@NLO 2.2.2[42,43] event generator at leading order (LO). The tt events are generated with up to three additional partons in the matrix element calculations, while up to four additional partons can be present for W þ jets, Z þ jets, and γ þ jets events. Single top quark events produced through the s channel, diboson events such as WW, ZZ, and ZH production, where H is a Higgs boson, and rare events such as ttW, ttZ, and WWZ production, are generated with this same program [42,44] at next-toleading (NLO) order, except that WW events in which both W bosons decay leptonically are generated using the POWHEG v2.0 [45][46][47][48][49] program at NLO. The same POWHEG generator is used to describe single top quark events produced through the t and tW channels. The detector response is modeled with the GEANT4 [50] suite of programs. Normalization of the simulated background samples is performed using the most accurate cross section calculations available [42,48,49,[51][52][53][54][55][56][57][58][59], which generally correspond to NLO or next-to-NLO precision.
Samples of simulated signal events are generated at LO using the MADGRAPH5_AMC@NLO program. Up to two additional partons are included in the matrix element calculation. The production cross sections are determined with NLO plus next-to-leading logarithmic (NLL) accuracy [60][61][62][63][64]. Events with gluino (squark) pair production are generated for a range of gluino mg (squark mq) and LSP mχ0 1 mass values, with mχ0 1 < mg (mχ0 1 < mq). The ranges of mass considered vary according to the model but are generally from around 600 to 2200 GeV for mg, 200 to 1700 GeV for mq, and 0 to 1200 GeV for mχ0 1 (see the results shown in Sec. VIII for more detail). For the T1tbtb model, the mass of the intermediateχ þ 1 state is taken to be mχ0 1 þ 5 GeV, while for the T5qqqqVV model, the masses of the intermediateχ 0 2 andχ þ 1 are given by the mean of mχ0 1 and mg. The gluinos and squarks decay according to phase space [65]. To render the computational requirements versus H T plane. Intervals 1 and 4 are discarded for N jet ≥ 7. The intervals labeled C1, C2, and C3 are control regions used to evaluate the QCD background. The rightmost and topmost bins are unbounded, extending to H T ¼ ∞ and H miss manageable, the detector response is described using the CMS fast simulation [66,67], which yields consistent results with the GEANT4-based simulation, except that we apply a correction of 1% to account for differences in the efficiency of the jet quality requirements [37], corrections of 5-12% to account for differences in the b jet tagging efficiency, and corrections of 0-14% to account for differences in the modeling of H T and H miss T . For simulated samples generated at LO (NLO), the NNPDF3.0LO [68] (NNPDF3.0NLO [68]) parton distribution functions (PDFs) are used. Parton showering and hadronization are described by the PYTHIA 8.205 [65] program for all samples.
To improve the description of initial-state radiation (ISR), we compare the MADGRAPH prediction to data in a control region enriched in tt events: two leptons (ee, μμ, or eμ) and two tagged b jets are required. The number of all other jets in the event is denoted N ISR jet . The correction factor is derived as a function of N ISR jet , with a central value ranging from 0.92 for N ISR jet ¼ 1 to 0.51 for N ISR jet ≥ 6. These corrections are applied to simulated tt and signal events. From studies with a single-lepton data control sample, dominated by tt events, the associated systematic uncertainty is taken to be 20% of the correction for tt events and 50% of the correction for signal events, where the larger uncertainty in the latter case accounts for possible differences between tt and signal event production.

VI. SIGNAL SYSTEMATIC UNCERTAINTIES
Systematic uncertainties in the signal event yield are listed in Table II. To evaluate the uncertainty associated with the renormalization (μ R ) and factorization (μ F ) scales, each scale is varied independently by a factor of 2.0 and 0.5 [69,70]. The uncertainties associated with μ R , μ F , and ISR, integrated over all search regions, typically lie below 0.1% but can be as large as the maximum values noted in Table II for Δm ≈ 0, where Δm is the difference between the gluino or squark mass and the sum of the masses of the particles into which it decays. For example, for the T1tttt model, Δm is given by where m top is the top quark mass. The uncertainties associated with the jet energy scale and jet energy resolution are evaluated as a function of jet p T and η. An uncertainty in the event yield associated with pileup is evaluated based on the observed distribution of the number N vtx of reconstructed vertices, and on the selection efficiency and its uncertainty determined from simulation as a function of N vtx . The isolatedlepton and isolated-track vetoes have a minimal impact on the T1bbbb, T1qqqq, T2bb, and T2qq models because events in these models rarely contain an isolated lepton. Thus, the associated uncertainty is negligible (≲0.1%). The systematic uncertainty in the determination of the integrated luminosity is 2.5% [71].
Systematic uncertainties in the signal predictions associated with the b jet tagging and misidentification efficiencies are also evaluated. These uncertainties do not affect the signal yield but can potentially alter the shape of signal distributions. The systematic uncertainties associated with the trigger, μ R , μ F , ISR, jet energy scale, jet energy resolution, statistical precision in the event samples, and H miss T modeling can also affect the shapes of the signal distributions. We account for these potential changes in shape, i.e., migration of events between search regions, in the limit-setting procedure described in Sec. VIII.

VII. BACKGROUND EVALUATION
The evaluation of background is primarily based on data control regions (CRs). Signal events, if present, could populate the CRs, an effect known as signal contamination. The impact of signal contamination is evaluated as described in Sec. VIII. Signal contamination is negligible for all CRs except those used to evaluate the top quark and W þ jets background (Sec. VII A). It is non-negligible only for the models that can produce an isolated track or lepton, viz., the T1tttt, T1tbtb, T5qqqqVV, and T2tt models, and the mixed models of gluino decays to heavy squarks described in the Introduction.

A. Background from top quark and W + jets events
The background from the SM production of tt, single top quark, and W þ jets events originates from W bosons that decay leptonically to yield a neutrino and a charged lepton. If the charged lepton is an electron or muon, including those from τ lepton decay, it is called a "lost" lepton. A lost TABLE II. Systematic uncertainties in the yield of signal events, averaged over all search regions. The variations correspond to different signal models and choices for the SUSY particle masses. Results reported as 0.0 correspond to values less than 0.05%. "Mixed T1" refers to the mixed models of gluino decays to heavy squarks described in the Introduction. lepton arises if an electron or muon lies outside the analysis acceptance, is not reconstructed, or is not isolated, and thus is not vetoed by the requirements of Sec. IV. The other possibility is that the charged lepton is a hadronically decaying τ lepton, denoted "τ h ."

Lost-lepton background
The procedure used to evaluate the lost-lepton background was described in Ref. [17] (see also Refs. [21,22,72]). Briefly, single-lepton CRs are selected using the standard trigger and selection criteria, except with the electron and muon vetoes inverted and the isolatedtrack veto not applied. Exactly one isolated electron or muon must be present. In addition, the transverse mass m T formed from the ⃗p miss T and lepton ⃗p T is required to satisfy m T < 100 GeV: this requirement is effective at identifying SM events, while reducing potential signal contamination. The T1tttt (T1tbtb, T5qqqqVV, T2tt) signal contamination in the resulting CRs is generally negligible (≲0.1%), but it can be as large as 30-50% (25-60%, 2-15%, 5-50%) for large values of N jet , N b-jet , H T , and/or H miss T , depending on mg or mq and mχ0 1 . Similar results to the T1tbtb model are obtained for the mixed models of gluino decay to heavy squarks.
Each CR event is entered into one of the 174 search regions with a weight that represents the probability for a lost-lepton event to appear with the corresponding values of H T , H miss T , N jet , and N b-jet . The weights are determined from the tt, W þ jets, single top quark, and rare process simulations through evaluation of the efficiency of the lepton acceptance, lepton reconstruction, lepton isolation, isolated-track, and m T requirements. Corrections are applied to account for the purity of the CR, the contributions of dilepton events to the signal regions and CR, and efficiency differences with respect to data. More details can be found in Ref. [17]. The efficiencies are determined as a function of H T , H miss T , N jet , N b-jet , lepton p T and η, and other kinematic variables. Improvements relative to Ref.
[17] are that we now use N b-jet and lepton η to help characterize the efficiencies, and the efficiency of the isolated-track veto is now determined separately for lostlepton events that fail the acceptance, reconstruction, or isolation requirements. Previously, only a single overall isolated-track veto efficiency was evaluated (as a function of search region) when constructing the weights.
The weighted distributions of the search variables, summed over the events in the CRs, define the lost-lepton background prediction. The procedure is performed separately for the single-electron and single-muon CRs, both of which are used to predict the total lost-lepton background, i.e., the background due both to lost electrons and to lost muons. The two predictions yield consistent results and are averaged, with correlations in the uncertainties taken into account, to obtain the final lost-lepton background estimate. The method is checked with a closure test, namely by determining the ability of the method, applied to simulated event samples, to predict correctly the true number of background events. The results of this test are shown in Fig. 3.
The dominant uncertainty in the lost-lepton background prediction is statistical, due to the limited number of CR events. As a systematic uncertainty, we take the larger of the observed nonclosure and the statistical uncertainty in the nonclosure, for each search region, where "nonclosure" refers to the bin-by-bin difference between the solid points and histogram in Fig. 3. Additional systematic uncertainties are evaluated as described in Ref.
[17] and account for potential differences between the data and simulation for the lepton acceptance, lepton reconstruction efficiency, lepton isolation efficiency, isolated-track efficiency, m T selection efficiency, dilepton contributions, and purity of the CRs.

Hadronically decaying τ lepton background
To evaluate the top quark and W þ jets background due to τ h events, a CR event sample is selected using a trigger that requires either at least one isolated muon candidate with p T > 24 GeV, or at least one isolated muon candidate with p T > 15 GeV in conjunction with H T > 500 GeV. The reason a special trigger is used, and not the standard one, is that the τ h background determination method requires there not be a selection requirement on missing transverse momentum, as is explained below. The selected The lost-lepton background in the 174 search regions of the analysis as determined directly from tt, single top quark, W þ jets, diboson, and rare-event simulation (points, with statistical uncertainties) and as predicted by applying the lost-lepton background determination procedure to simulated electron and muon control samples (histograms, with statistical uncertainties). The results in the lower panel are obtained through bin-by-bin division of the results in the upper panel, including the uncertainties, by the central values of the "predicted" results. The ten results (eight results for N jet ≥ 7) within each region delineated by vertical dashed lines correspond sequentially to the ten (eight) kinematic intervals of H T and H miss events are required to contain exactly one identified muon with jηj < 2.1. The p T of the muon candidate must exceed 20 GeV, or 25 GeV if H T < 500 GeV. The fraction of T1tttt (T1tbtb, T5qqqqVV, T2tt) events in the CR due to signal contamination is generally ≲0.1%, but can be as large as 5-22% (1-20%, 1-15%, 1-40%) for large values of N jet , N b-jet , H T , and/or H miss T , depending on mg or mq and mχ0 1 , with similar results to the T1tbtb model for the mixed models of gluino decay to heavy squarks.
The τ h background is determined using the method described in Ref.
[17] (see also Refs. [21,22,72]). It makes use of the similarity between μ þ jets and τ h þ jets events aside from the detector response to the μ or τ h . In each CR event, the muon p T is smeared through random sampling of τ h response functions derived from simulation of single W → τ h ν τ decay events. This differs from Ref.
[17], in which W → τ h ν τ decays in simulated tt and W þ jets events were used to derive the response functions. The change was made in order to reduce the risk of contamination in the response functions from nearby nonτ h -related particles; note that the CR already includes the effects from the underlying event and nearby jets. The response functions express the expected visible-p T distribution of a τ h candidate as a function of the true τ lepton p T , taken to be the measured muon p T in the CR event. Following the smearing, the values of H T , H miss T , N jet , and N b-jet are calculated for the CR event, and the selection criteria of Sec. IV are applied. Note that CR events with relatively low values of H miss T can be promoted, after smearing, to have H miss T values above the nominal threshold, and thus appear in the τ h background prediction. It is for this reason that the CR is selected using a trigger without a requirement on missing transverse momentum: to avoid possible H miss T bias. The probability for a τ h jet to be erroneously identified as a b jet is taken into account. Corrections are applied to account for the trigger efficiency, the acceptance and efficiency of the μ selection, and the ratio of branching fractions BðW → τ h νÞ=BðW → μνÞ ¼ 0.65 [73]. The resulting event yield provides the τ h background estimate. The method is validated with a closure test, whose results are shown in Fig. 4.
Systematic uncertainties are assigned based on the level of nonclosure, as described for the lost-lepton background. In addition, systematic uncertainties are evaluated for the muon reconstruction, isolation, and acceptance efficiencies, for the response functions, and for the misidentification rate of τ h jets as b jets. The dominant source of uncertainty, as for the lost-lepton background, is from the limited statistical precision of the CR sample.

B. Background from Z → νν events
The evaluation of background from SM Z þ jets events with Z → νν is based on CR samples of γ þ jets events, and of Z þ jets events with Z → l þ l − (l ¼ e, μ). The photon in the γ þ jets events and the l þ l − pair in the Z → l þ l − events are removed from the event in order to emulate missing transverse momentum. The γ þ jets and Z → l þ l − events are then subjected to the same selection criteria as in the standard analysis, with corrections applied to account for differences in acceptance with respect to the Zð→ ννÞ þ jets process. The use of γ þ jets events exploits the similarity between Z boson and direct photon production in pp collisions, where "direct" refers to a photon produced through the Compton scattering (qg → qγ) or annihilation (qq → gγ) process.
The method is an extension of that described in Ref. [17]. Briefly, the relatively copious γ þ jets events are used to evaluate the background in the 46 search regions with N b-jet ¼ 0. We do not use γ þ jets events for the N b-jet > 0 search regions to avoid reliance on the theoretical modeling of γ þ jets versus Z þ jets production with bottom quarks. The less abundant Z → l þ l − events are used to validate and calibrate the N b-jet ¼ 0 results, as described below, and to extrapolate to the N b-jet > 0 search regions. For this extrapolation, the Z → l þ l − data are integrated over H T and H miss T because of the limited number of events.
The Z → l þ l − CR sample is selected using a combination of triggers that requires either i) at least one isolated electron or muon with p T > 15 GeV, and either H T > 350 or 400 GeV depending on the LHC instantaneous luminosity, ii) at least one electron with either p T > 105 or 115 GeV depending on the instantaneous luminosity, iii) at least one muon with p T > 50 GeV, or iv) at least one  isolated electron (muon) with p T > 27 (24) GeV. The events are required to contain exactly one e þ e − or one μ þ μ − pair with an invariant mass within 15 GeV of the nominal Z boson mass, with the constituents of the pair identified using the same criteria for isolated electrons and muons as in the standard analysis. The p T of the lepton pair must exceed 200 GeV. To ensure that the Z → l þ l − and γ þ jets CRs are independent, a veto is applied to events containing an identified photon.
The γ þ jets CR sample is selected with a trigger that requires a photon candidate with p T > 175 GeV. Events are retained if they contain exactly one well-identified isolated photon with p T > 200 GeV. The photon isolation criteria require the pileup-corrected energy within a cone of radius 0.3 around the photon direction, excluding the energy carried by the photon candidate itself, to satisfy upper bounds that depend on the p T and η of the photon, and are determined separately for the contributions of electromagnetic, charged hadronic, and neutral hadronic energy. About 85% of the events in the resulting sample are estimated to contain a direct photon, while the remaining events either contain a fragmentation photon, i.e., emitted as initial-or finalstate radiation or during the hadronization process, or a nonprompt photon, i.e., from unstable hadron decay. A fit to the photon isolation variable is performed as a function of H miss T to determine the photon purity β γ , defined as the fraction of events in the γ þ jets CR with a direct or fragmentation photon (these two types of photons are experimentally indistinguishable and together are referred to as "prompt").
The estimated number N pred Z→νν of Zð→ ννÞ þ jets background events contributing to each N b-jet ¼ 0 search region is given by where N obs γ is the number of events in the corresponding N jet , H T , and H miss T bin of the γ þ jets CR, β γ is the fraction that are prompt, F sim dir is the fraction of prompt photons that are also direct (evaluated from simulation), and R sim Z→νν=γ is the ratio from simulation of the number of Zð→ ννÞ þ jets events to the number of direct-photon γ þ jets events, with the direct photon term obtained from an LO MADGRAPH5_AMC@NLO calculation. The C γ data=sim factors are corrections to the simulation that account for efficiency differences in photon reconstruction with respect to data.
The ρ factor in Eq. (1) is determined from Z → l þ l − data and is used to account for potential differences between simulation and data in the R Z→νν=γ ratio, such as those that might be present because of missing higherorder corrections in the simulated γ þ jets term. It is given by where N obs Z→l þ l − , N sim Z→l þ l − , and N sim γ are the numbers of events in the indicated CRs, with the simulated samples normalized to the integrated luminosity of the data. The sums and averages span the search regions. The β data ll factors represent the purity of the Z → l þ l − CR, obtained from fits to the measured lepton-pair mass distributions, while C ll data=sim are corrections to account for data-versus-simulation differences in lepton reconstruction efficiencies. While the Z → l þ l − sample is too small to allow a meaningful measurement of ρ in each search region, we examine the projections of ρ in each dimension. We find a modest dependence on H T and on the correlated variable N jet . Based on the observed empirical result ρðH T Þ ¼ 0.91 þ ð9.6 × 10 −5 GeV −1 Þ min ðH T ; 900 GeVÞ, we apply a weight to each simulated γ þ jets event entering the evaluation of ρ and R Z→νν=γ . Following this weighting, the projections of ρ in the N jet , H T , and H miss T dimensions are consistent with a constant value of 1.00, with uncertainties deduced from linear fits to the projections that vary with these variables between 2 and 13%. For where j, b, and k are bin indices (numbered from zero) for the N jet , N b-jet , and kinematic (i.e., H T and H miss T ) variables, respectively. For example, j ¼ 1 corresponds to Table I and Fig. 2. The first term on the righthand side of Eq. (3) is obtained from Eq. (1).
For all but the N jet ≥ 9 bin, corresponding to j ¼ 4, the N b-jet extrapolation factor F j;b is obtained from the fitted Z → l þ l − data yields, with data-derived corrections β data ll to account for the N b-jet -dependent purity. Other efficiencies cancel in the ratio. Specifically, For N jet ≥ 9, there are very few Z → l þ l − events and we use the measured results for N jet ¼ 7-8 (the j ¼ 3 bin) multiplied by an N b-jet extrapolation factor from simulation: A systematic uncertainty is assigned to the ratio of simulated yields in Eq. (5) based on a lower bound equal to 1.0 and an upper bound determined using the binomial model of Ref.
[17]. The resulting uncertainty ranges from 7 to 40%, depending on N b-jet . A closure test of the method is presented in Fig. 5. The shaded bands represent systematic uncertainties of 7, 10, and 20% for N b-jet ¼ 1, 2, and ≥ 3, respectively, combined with the statistical uncertainties from the simulation. The systematic uncertainties account for the assumption that the F j;b terms are independent of H T and H miss T . The rare process ttZ and the even more rare processes ZZ, WWZ, WZZ, and ZZZ can contribute to the background. We add the expectations for these processes, obtained from simulation, to the numerator and denominator of Eq. (5). Note that processes with a Z boson that have a counterpart with the Z boson replaced by a photon are already accounted for in N obs γ and largely cancel in the R Z→νν=γ ratio. For search regions with N jet ≥ 9 and N b-jet ≥ 2, the contribution of ttZ events is comparable to that from Z þ jets events, with an uncertainty of ≈50%, consistent with the rate and uncertainty for ttZ events found in Ref. [74].
Besides the uncertainties associated with the N b-jet extrapolation and the ρ term, discussed above, systematic uncertainties associated with the statistical precision of the simulation, the photon reconstruction efficiency, the photon and dilepton purities, and the R sim Z→νν=γ term are evaluated. The principal uncertainty arises from the limited number of events in the CRs.

C. Background from QCD events
Background from QCD events is not, in general, expected to be large. Nonetheless, since H miss T in these events primarily arises from the mismeasurement of jet p T rather than from genuine missing transverse momentum, it represents a difficult background to model. We employ two methods, complementary to each other, to evaluate the QCD background: the rebalance-and-smear (R&S) method [21,22] and the low-Δϕ extrapolation method [17,75]. The R&S method is selected as our primary technique because it is more strongly motivated from first principles and is less empirical in nature. Thus the R&S method is used for the interpretation of the data, presented in Sec. VIII. The low-Δϕ extrapolation method is used as a cross-check.

The rebalance-and-smear method
The R&S method utilizes a special CR event sample, selected using triggers that require H T to exceed thresholds ranging from 250 to 800 GeV.
In a first step, called "rebalance," the jet momenta in a CR event are rescaled to effectively undo the effects of detector response. This step is performed using Bayesian inference. The prior probability distribution π is derived from the particle-level QCD simulation, where "particle level" corresponds to the level of an event generator, i.e., without simulation of the detector. It is given by where PðH miss T Þ is the distribution of H miss T , and PðΔϕ H miss T ;j 1ðbÞ Þ is the distribution of the azimuthal angle between ⃗ H miss T and the highest p T jet in the event, or between ⃗ H miss T and the highest p T tagged b jet if N b-jet ≥ 1. The prior is binned in intervals of H T and N b-jet . The prior thus incorporates information about both the magnitude and direction of the genuine ⃗ H miss T expected in QCD events. This represents a more sophisticated treatment than the one used in Refs. [21,22], where the prior was merely taken to be a Dirac delta function at H miss The jets in a CR event are then rescaled, using Bayes' theorem, to represent the event at the particle level. Jets with p T > 15 GeV and jηj < 5.0 are included in this procedure. The expression of Bayes' theorem is  The Z → νν background in the 174 search regions of the analysis as determined directly from Zð→ ννÞ þ jets simulation (points, with statistical uncertainties), and as predicted by applying the Z → νν background determination procedure to statistically independent Zð→ l þ l − Þ þ jets simulated event samples (histogram, with shaded regions indicating the quadrature sum of the systematic uncertainty associated with the assumption that F j;b is independent of H T and H miss T , and the statistical uncertainty). For bins corresponding to N b-jet ¼ 0, the agreement is exact by construction. The results in the lower panel are obtained through bin-by-bin division of the results in the upper panel, including the uncertainties, by the central values of the "predicted" results. The labeling of the bin numbers is the same as in Fig. 3. determined in bins of jet p T and η, are derived from simulation as the distribution of the ratio of reconstructed jet p T values to a given generated value, corrected with separate scale factors for the Gaussian cores and non-Gaussian tails to account for jet energy resolution differences with respect to data. The likelihood function is maximized by rescaling the momenta of the measured jets, with the respective jet p T uncertainties as constraints. The set ⃗ J part corresponding to the resulting most-likely posterior probability defines the rebalanced event.
In a second step, denoted "smear," the magnitudes of the jet momenta are rescaled by p T -and η-dependent factors obtained from random sampling of the jet response functions. This sampling is performed numerous times for each rebalanced event to increase the statistical precision of the resulting sample. Each event is weighted with a factor inversely proportional to the number of times it is sampled.
Application of the R&S procedure produces an event sample that closely resembles the original sample of CR events, except the contributions of events with genuine H miss T , viz., top quark, W þ jets, Z þ jets, and possible signal events, are effectively eliminated [21]. The rebalanced and smeared events are subjected to the standard event selection criteria of Sec. IV to obtain the predictions for the QCD background in each search region.
The principal uncertainty in the R&S QCD background prediction is systematic, associated with the uncertainty in the shape of the jet response functions. This uncertainty is evaluated by varying the jet energy resolution scale factors within their uncertainties, resulting in uncertainties in the prediction that range from 20-80% depending on the search region. Smaller uncertainties related to the trigger, the prior, and the statistical uncertainties are also evaluated.
As a test of the method, we determine the R&S prediction for the QCD contribution to a QCD-dominated CR selected with the standard trigger and event selection, except for the Δϕ H miss T ;j i requirements of Sec. IV, which are inverted. Specifically, at least one of the two (for N jet ¼ 2), three (for N jet ¼ 3), or four (for N jet ≥ 4) highest p T jets in an event must fail a Δϕ H miss T ;j i selection criterion. The resulting QCD-dominated sample is called the low-Δϕ CR. The R&S prediction for the QCD background in the low-Δϕ CR is shown in Fig. 6 in comparison to the corresponding measured results, following subtraction from the data of the contributions from top quark, W þ jets, and Z þ jets events, evaluated as described in the previous sections. Note that because of this subtraction, the resulting difference is sometimes negative. The prediction from the R&S method is seen to agree with the data within the uncertainties.

The low-Δϕ extrapolation method
In the low-Δϕ extrapolation method, the QCD background in each search region is evaluated by multiplying the observed event yield in the corresponding region of the low-Δϕ CR (Sec. VII C 1), after accounting for the contributions of non-QCD SM events, by a factor R QCD determined primarily from data. The R QCD terms express the ratio of the expected QCD background in the corresponding signal and low-Δϕ regions.
The R QCD term is empirically observed to have a negligible dependence on N b-jet for a given value of N jet . The functional dependence of R QCD can therefore be expressed in terms of H T , H miss T , and N jet alone. The R QCD term is modeled as where i, j, and k are the H T , N jet , and H miss T bin indices, respectively. In Ref.
[17] we used a model in which the H T , H miss T , and N jet dependencies in R QCD factorized. For the N jet ¼ 2 search regions, introduced for the present study, this factorization is found to be less well justified and we adopt the parametrization of Eq. (8).
The K data ij factors are determined from a maximum likelihood fit to data in a sideband region defined by 250 < H miss T < 300 GeV (regions C1, C2, and C3 in Fig. 2). They are the ratio of the number of QCD events in the high-Δϕ region to that in the low-Δϕ region, where "high Δϕ" refers to events selected with the standard (noninverted) Δϕ H miss T ;j i requirements. The fit accounts for the contributions of top quark, W þ jets, and Z þ jets events using the results of the methods described in the preceding sections. Uncertainties in K data ij are determined from the covariance matrix of the fit. The S sim ik terms, taken from the QCD simulation, represent corrections to account for the H miss  6. The QCD background in the low-Δϕ CR as predicted by the R&S method (histograms, with statistical and systematic uncertainties added in quadrature), compared to the corresponding data from which the expected contributions of top quark, W þ jets, and Z þ jets events have been subtracted (points, with statistical uncertainties). The lower panel shows the ratio of the measured to the predicted results and its propagated uncertainty. The labeling of the bin numbers is the same as in Fig. 3. of R QCD . Based on studies of the differing contributions of events in which the jet with the largest p T mismeasurement is or is not amongst the two (for N jet ¼ 2), three (for N jet ¼ 3), or four (for N jet ≥ 4) highest p T jets, uncertainties between 14 and 100% are assigned to the S sim ik terms to account for potential differences between data and simulation. The total uncertainties in S sim ik are defined by the sum in quadrature of the systematic uncertainties and the statistical uncertainties from the simulation. Figure 7 presents a closure test for the method. An additional systematic uncertainty is included in R QCD to account for the level of nonclosure. Figure 8 shows a comparison between the predictions of the R&S and Δϕ methods, which are seen to be consistent. Residual differences between the results from the two methods are negligible compared to the overall uncertainties. Figure 9 presents the observed numbers of events in the 174 search regions. The data are shown in comparison with the summed predictions for the SM backgrounds. Numerical values are given in Tables VI-X of Appendix B. Signal region 126 exhibits a difference of 3.5 standard deviations with respect to the SM expectation. Signal regions 74, 114, and 151 exhibit differences between 2 and 3 standard deviations. The differences for all other signal regions lie below 2 standard deviations. Thus, the evaluated SM background is found to be statistically compatible with the data and we do not obtain evidence for supersymmetry.

VIII. RESULTS
In addition to the finely segmented search regions of Fig. 9, we evaluate the background predictions in 12 aggregate regions, determined by summing the results from the nominal search regions while accounting for correlations. The aggregate regions are intended to represent 12 potentially interesting signal topologies. For representative values of the SUSY particle masses, the cross section upper limits from individual aggregate signal regions are found to be around 50-300% larger than those presented below for the full 174 bin fit, with a typical difference of about 100%. Nonetheless, the limits on SUSY particle masses derived using the aggregate regions are generally no more than around 10% lower than those found using the fit based on the 174 regions. While the aggregate regions do not provide as much sensitivity to the presence of new physics as the full set of search regions, they allow our data to be used in a simpler manner for the investigation of signal scenarios not examined in this paper. The aggregate regions, and the signal topologies they are intended to help probe, are specified in Table III. The aggregate regions are characterized by their heavy flavor (top or bottom quark) content, parton multiplicity, and the mass difference Δm discussed in Sec. VI. Aggregate regions 11 and 12 target models with direct top squark production. The results for the aggregate regions are presented in Fig. 10, with numerical values provided in Table XI of Appendix B.
In Fig. 11, for purposes of illustration, we present onedimensional projections of the data and SM predictions in either the H miss T , N jet , or N b-jet variable after imposing criteria, indicated in the legends, to enhance the expected contributions of T1tttt, T1bbbb, T1qqqq, T2tt, T2bb, or T2qq events. In each case, two example signal distributions are shown: one with Δm ≫ 0, and one with Δm ≈ 0, where both example scenarios lie well within the parameter space excluded by the present study.
Limits are evaluated for the production cross sections of the signal scenarios using a likelihood fit, with the SUSY signal strength, the yields of the four classes of background shown in Fig. 9, and various nuisance parameters as fitted parameters, where a nuisance parameter refers to a variable of little physical interest, such as a scale factor in a background determination procedure. The nuisances are constrained in the fit. For the models of gluino (squark) pair production, the limits are derived as a function of m~g (mq) and mχ0 1 . All 174 search regions are used for each choice of the SUSY particle masses. The likelihood function is given by the product of Poisson probability density functions, one for each search region, and constraints that account for uncertainties in the background predictions and signal yields. These uncertainties are treated as nuisance parameters with log-normal probability density functions. Correlations are taken into account. The signal yield uncertainties associated with the renormalization and factorization scales, ISR, jet energy scale, b jet tagging, pileup, and statistical fluctuations are evaluated as a function of m~g and mχ0 1 , or mq and mχ0 1 . The test statistic is q μ ¼ −2 ln ðL μ =L max Þ, where L max is the maximum likelihood determined by allowing all parameters including the SUSY signal strength μ to vary, and L μ is the maximum    1 . The thick solid (black) curves show the observed exclusion limits assuming the NLO þ NLL cross sections [60][61][62][63][64] and the thin solid (black) curves show the change in these limits due to variation of the signal cross sections within their theoretical uncertainties [79]. The thick dashed (red) curves present the expected limits under the background-only hypothesis, while the thin dotted (red) curves indicate the region containing 68% of the distribution of limits expected under this hypothesis. Lower right: The corresponding 95% NLO þ NLL exclusion curves for the mixed models of gluino decays to heavy squarks. For the T1tbtb model, the results are restricted to mχ0 1 > 25 GeV for the reason stated in the text.
likelihood for a fixed signal strength. To set limits, asymptotic results for the test statistic [76] are used, in conjunction with the CL s criterion described in Refs. [77,78]. We evaluate 95% confidence level (C.L.) upper limits on the signal cross sections. The NLO þ NLL cross section is used to determine corresponding exclusion curves. When computing the limits, the signal yields are corrected to account for possible signal contamination in the CRs. Beyond the observed exclusion limits, we derive expected exclusion limits by using the expected Poisson fluctuations around the predicted numbers of background events when evaluating the test statistic.
The results for the T1tttt, T1bbbb, T1qqqq, and T5qqqqVV models are shown in the upper and middle rows of Fig. 12. Depending on the value of mχ0 1 , and using

95% CL upper limit on cross section [pb]
[GeV] Note that for the T2tt model we do not present cross section upper limits in the unshaded diagonal region at low mχ0 1 for the reasons discussed in the text, and that there is a small region corresponding to m~t ≲ 230 GeV and mχ0 1 ≲ 20 GeV that is not included in the NLO þ NLL exclusion region. The results labeled "one lightq " for the T2qq model are discussed in the text. The meaning of the curves is described in the caption of Fig. 12. the NLO þ NLL cross sections, gluinos with masses as large as 1960, 1950, 1825, and 1800 GeV, respectively, are excluded. These results significantly extend those of our previous study [17], for which the corresponding limits vary between 1440 and 1600 GeV.
The corresponding results for the T1tbtb model and for the mixed models of gluino decay to heavy squarks are shown in the lower row of Fig. 12. In this case gluinos with masses as large as 1850 to 1880 GeV are excluded, extending the limits of between 1550 and 1600 GeV presented in Ref. [19]. Note that for the T1tbtb model, the acceptance is small for mχ0 1 ≲ 25 GeV and we are unable to exclude the scenario. The reason is that as mχ0 1 approaches zero, the mass of the nearly mass-degenerateχ þ 1 parent particle also becomes small. Theχ þ 1 becomes highly Lorentz boosted, and more of the momentum from the parentχ þ 1 is carried by the daughter off-shell W boson [see Fig. 1 (upper right)] and less by the daughterχ 0 1 . The net effect is that the H miss T spectrum becomes softer for hadronic W Ã decays, leading to reduced signal acceptance, while the charged-lepton or isolated-track p T spectrum becomes harder for leptonic W Ã decays, increasing the probability for the event to be vetoed and thus also leading to reduced signal acceptance. Furthermore, jets arising from the W Ã decay tend to be aligned with the missing transverse momentum from theχ 0 1 . When these jets become harder, as mχ0 1 becomes small, they are more likely to appear amongst the highest p T jets in the event, causing the event to be rejected by the Δϕ H miss T ;j i requirements. Because of the small signal acceptance for mχ0 1 → 0, the relative contribution of signal contamination in this region becomes comparable to the true signal content, and a precise determination of the search sensitivity becomes difficult. Therefore, for the T1tbtb model, we limit our determination of the cross section upper limit to mχ0 1 > 25 GeV. Finally, Fig. 13 shows the results for the T2tt, T2bb, and T2qq models. Based on the NLO þ NLL cross sections, squarks with masses up to 960, 990, and 1390 GeV, respectively, are excluded. Note that for the T2tt model we do not present cross section upper limits for small values of mχ0 1 if mq − mχ0 1 ≈ m top , corresponding to the unshaded diagonal region at low mχ0 1 visible in Fig. 13  (upper left). The reason for this is that signal events are essentially indistinguishable from SM tt events in this region, rendering the signal event acceptance difficult to model. Note also for the T2tt model that there is a small region corresponding to m~t ≲ 230 GeV and mχ0 1 ≲ 20 GeV that is not excluded by the data.
In addition to the main T2qq model, with four massdegenerate squark flavors (up, down, strange, and charm), each arising from two different quark spin states, Fig. 13 (lower) shows the results should only one of these eight states ("one lightq ") be accessible at the LHC. In this case, the upper limit on the squark mass based on the NLO þ NLL cross section is reduced to 950 GeV.

IX. SUMMARY
A search for gluino and squark pair production was presented based on a sample of proton-proton collisions collected at a center-of-mass energy of 13 TeV with the CMS detector. The search was performed in the multijet channel, i.e., the visible reconstructed final state consists solely of jets. The data correspond to an integrated luminosity of 35.9 fb −1 . Events were required to have at least two jets, H T > 300 GeV, and H miss T > 300 GeV, where H T is the scalar sum of jet transverse momenta p T . The H miss T variable, used as a measure of missing transverse momentum, is the magnitude of the vector p T sum of jets. Jets were required to have p T > 30 GeV and to appear in the pseudorapidity range jηj < 2.4.
The data were examined in 174 exclusive four-dimensional search regions defined by the number of jets, the number of tagged bottom quark jets, H T , and H miss T . Background from standard model processes was evaluated using control samples in the data. We also provided results for 12 aggregated search regions, to simplify use of our data by others. The estimates of the standard model background were found to agree with the observed numbers of events for all regions.
The results were interpreted in the context of simplified models. We considered models in which pair-produced gluinos each decay to a tt pair and an undetected, stable, LSP neutralinoχ 0 1 (T1tttt model); to a bb pair and theχ 0 1 (T1bbbb model); to a light-flavored qq pair and theχ 0 1 (T1qqqq model); to a light-flavored quark and antiquark and either the second-lightest neutralinoχ 0 2 or the lightest charginoχ þ 1 , followed by decay of theχ 0 2 (χ þ 1 ) to theχ 0 1 and an on-or off-shell Z (W AE ) boson (T5qqqqVV model); or tō tbχ þ 1 or tbχ − 1 , followed by the decay of theχ þ 1 to theχ 0 1 and an off-shell W boson (T1tbtb model). To provide more model independence, we also considered mixed scenarios in which a gluino can decay to ttχ 0 1 , bbχ 0 1 ,tbχ þ 1 , or tbχ − 1 with various probabilities. Beyond the models for gluino production, we examined models for direct squark pair production. We considered scenarios in which each squark decays to a top quark and theχ 0 1 (T2tt model); to a bottom quark and theχ 0 1 (T2bb model); or to a light-flavored (u, d, s, c) quark and theχ 0 1 (T2qq model). We derived upper limits at the 95% confidence level on the model cross sections as a function of the gluino and LSP masses, or of the squark and LSP masses.
Using the predicted cross sections with next-to-leadingorder plus next-to-leading-logarithm accuracy as a reference, 95% confidence level lower limits on the gluino mass as large as 1800 to 1960 GeV were derived, depending on the scenario. The corresponding limits on the mass of directly produced squarks range from 960 to 1390 GeV. These results extend those from previous searches.

Bundes-ministerium
Forschungs-gemeinschaft Forschungs-zentren Rachada-pisek We congratulate our colleagues in the CERN accelerator departments for the excellent performance of the LHC and thank the technical and administrative staffs at CERN and at other CMS institutes for their contributions to the success of the CMS effort. In addition, we gratefully acknowledge the computing centers and personnel of the Worldwide LHC Computing Grid for delivering so effectively the computing infrastructure essential to our analyses. Finally, we acknowledge the enduring support for the construction and operation of the LHC and the CMS detector provided by the following funding agencies: the Austrian  Tables IV and V present cumulative selection efficiencies for representative simplified models of gluino and squark pair  production, respectively.   TABLE IV. Absolute cumulative efficiencies in % for each step of the event selection process for representative models of gluino pair production. The uncertainties are statistical. Uncertainties reported as 0.0 correspond to values less than 0.05%. pp →gg;g → ttχ 0 1 pp →gg;g → bbχ 0 1 pp →gg;g → qqχ 0   V. Absolute cumulative efficiencies in % for each step of the event selection process for representative models of squark pair production. The uncertainties are statistical. Uncertainties reported as 0.0 correspond to values less than 0.05%.

APPENDIX B: PREFIT BACKGROUND PREDICTIONS
Tables VI-X present the prefit predictions for the number of standard model background events in each of the 174 search regions of the analysis, along with the observed numbers of events, where "prefit" means there is no constraint from the likelihood fit. The corresponding information for the 12 aggregate search regions is presented in Table XI. TABLE VI. Observed numbers of events and prefit background predictions in the N jet ¼ 2 search regions. The first uncertainty is statistical and the second is systematic. Obs.