Search for supersymmetry in proton-proton collisions at 13 TeV in final states with jets and missing transverse momentum

Results are reported from a search for supersymmetric particles in the final state with multiple jets and large missing transverse momentum. The search uses a sample of proton-proton collisions at $\sqrt{s}=$ 13 TeV collected with the CMS detector in 2016-2018, corresponding to an integrated luminosity of 137 fb$^{-1}$, representing essentially the full LHC Run 2 data sample. The analysis is performed in a four-dimensional search region 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 significant excess in the event yield is observed relative to the expected background contributions from standard model processes. Limits on the pair production of gluinos and squarks are obtained in the framework of simplified models for supersymmetric particle production and decay processes. Assuming the lightest supersymmetric particle to be a neutralino, lower limits on the gluino mass as large as 2000 to 2310 GeV are obtained at 95% confidence level, while lower limits on the squark mass as large as 1190 to 1630 GeV are obtained, depending on the production scenario.


Introduction
The search for particles and interactions beyond the standard model (SM) is a major goal of experiments at the CERN LHC. The search described here focuses on experimental signatures in which a proton-proton (pp) collision produces at least two jets (collimated sprays of particles), in conjunction with large unbalanced ("missing") momentum in the direction transverse to the beam axis. The jets result from the production and hadronization of energetic quarks or gluons that could be generated in the decay chains of new heavy particles. The jets are classified according to whether their properties are consistent with a jet initiated by the production of a bottom quark (b jet), a key experimental signature in many models of new-particle production. The large missing transverse momentum is typically associated with the production of a stable, weakly interacting particle that is not detected by the apparatus. In this analysis, this quantity is inferred from the total momentum of the observed jets in the transverse plane, which should sum to approximately zero if there are no unobserved particles. Signatures of this type have been studied extensively by both the ATLAS and CMS Collaborations [1][2][3][4][5][6][7]. This signature arises frequently in theoretical models based on supersymmetry (SUSY) [8][9][10][11][12][13][14][15][16][17] as well as in a broad range of other theories [18][19][20][21][22][23] extending the SM.
The analysis uses a sample of pp collision events at √ s = 13 TeV recorded with the CMS detector in 2016-2018, corresponding to an integrated luminosity of 137 fb −1 . This represents essentially the complete CMS Run 2 data sample and is about four times larger than the 2016 data sample alone, which was used in the previous analysis based on this methodology [7].
The motivation for searches for new physics in the final state with jets and large missing transverse momentum arises from several considerations. Astrophysical observations provide compelling evidence for the existence of dark matter, known empirically to be the dominant component of matter in the universe. A weakly interacting massive particle (WIMP) is one class of candidates for dark matter. However, the SM does not contain such a particle. Within the SM, the Higgs boson presents special theoretical challenges. Assuming that the Higgs boson is a fundamental particle, its spin-0 nature implies that the physical mass of the Higgs boson, as a quantity in the SM, is unstable against corrections from quantum-loop processes. In the absence of extreme fine tuning [24][25][26][27] that would precisely cancel these effects, the Higgs boson mass is generically driven to the cutoff scale of validity of the theory, which could be as high as the Planck scale of quantum gravity. The instability of the Higgs boson mass, and with it, that of the entire electroweak scale (including the W and Z boson masses), is known as the gauge hierarchy problem. This problem has been a major challenge confronting theoretical particle physics for several decades. The discovery by ATLAS and CMS of a Higgs boson with a mass around 125 GeV has strongly highlighted this puzzle. The concept of "naturalness," [25][26][27], which refers to the degree of fine tuning of parameters, has been discussed extensively as an important, yet difficult to quantify, consideration in assessing theoretical scenarios.
Theories postulating physics beyond the SM, such as SUSY, can potentially address these problems. Supersymmetry relates each SM bosonic field degree of freedom to a corresponding fermionic superpartner field, and vice versa. Each spin J = 1/2 particle in the SM (the quarks and leptons) therefore has a spin J = 0 superpartner, so the SUSY spectrum contains a large number of scalar quarks (squarks, q) and scalar leptons (sleptons, l). The SUSY partners of the SM gauge bosons (J = 1) are referred to as gauginos (J = 1/2). For example, the superpartner of the gluon is a gluino ( g). The minimal supersymmetric SM (MSSM) [15][16][17] contains five Higgs bosons (J = 0) plus the usual four electroweak gauge bosons (J = 1) of the SM. In the MSSM, the partners of the Higgs and gauge bosons map onto a set of four J = 1/2 higgsinos and four electroweak gauginos. Because of possible mixing among these particles, these superpartners are generically referred to as electroweakinos, four of which are electrically neutral (neutralinos, χ 0 i , i = 1, . . . , 4) and four of which are charged (charginos, χ ± j , j = 1, 2). Supersymmetry provides a dark matter candidate if the lightest supersymmetric particle (LSP) is stable and has no electric or color charge. Stability of the LSP is guaranteed if the model conserves R parity [14,28], which also implies that SUSY particles are produced in pairs. In this scenario, which is assumed in this paper, the lightest neutralino χ 0 1 is the LSP and could be a WIMP dark matter candidate.
Because gluinos and squarks carry color charges, like their SM partners, they can be produced via the strong interaction: they therefore have the highest production cross sections among SUSY particles for a given mass. The absence of signals for these particles has so far led to lower limits on their masses of roughly m g ≈ 2 TeV for gluinos and m q ≈ 1 TeV for light-flavored squarks [1][2][3][4][5][6][7], although these results are model dependent. The present search focuses on processes involving the production of colored SUSY particles, either gluinos or squarks. Once the SUSY particles are produced, they typically decay via a sequence of processes that generates jets, leptons, and large missing transverse momentum (p miss T ). Large p miss T is a feature of models in which the masses involved in the decay chains allow the LSP to carry substantial transverse momentum (p T ). So that this study is orthogonal to ones explicitly requiring leptons, and to help enable a well-structured and independent set of SUSY searches in CMS, the present search vetoes events in which leptons (electrons or muons) are detected above a certain threshold in p T .
The basic approach of the analysis involves defining search regions in a four-dimensional space specified by key event variables that characterize the topology and kinematics of the events: the total number of jets (N jet ), the number of tagged b jets (N b-jet ), the scalar sum of jet p T (H T ), and the magnitude of the vector p T sum of the jets (H miss T ). The H miss T variable is used to estimate the p miss T present in the event. In total, there are 174 exclusive analysis bins in the four-dimensional search region, which together provide sensitivity to a wide range of SUSY scenarios.
In each of the 174 analysis bins, the background from SM processes is evaluated using event yields measured in corresponding control samples in the data, in conjunction with correction factors obtained from Monte Carlo (MC) simulated event samples. The principal sources of background arise from several SM processes: production of a top quark, either through top quark-antiquark (tt) pair production or, less often, a single top quark; production of an on-or off-mass-shell W or Z boson (W+jets and Z+jets events, respectively); and production of multijet events through quantum chromodynamics (QCD) processes. Both top quark and W+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-of-acceptance charged lepton, including a τ lepton with either a leptonic or hadronic decay. These backgrounds are determined using a single-lepton control sample. Similarly, Z+jets events can exhibit significant H miss T if the Z boson decays to two neutrinos. This background is determined using a control sample of γ+jets events, in conjunction with a control sample in which a Z boson decays into an e + e − or µ + µ − pair. Significant H miss T in QCD multijet events can arise if the p T of a jet is mismeasured, if a jet falls outside the acceptance of the jet selection, or from b jets that produce one or more neutrinos. The QCD background contribution is evaluated using specially defined control samples together with the "rebalance and smear" technique [7,29,30].
The search is performed using methodologies similar to those presented in Ref. [7]. The search regions, however, have been optimized for the larger amount of data, and refinements to the background estimation procedures have been implemented. The main difference with respect to Ref. [7] is that for the evaluation of background from top quark and W+jets events, we now  implement a transfer factor method rather than construct event-by-event background predictions separately for events with a hadronic tau lepton decay and for events with a electron or muon. Also, the larger data set of the current analysis allows us to evaluate the background from Z(→ νν )+jets events, in the cases with N b-jet > 0, using extrapolation factors based entirely on data, rather than relying on simulation for these extrapolations when N jet ≥ 9.
The interpretation of the results is performed using a set of representative SUSY models, each of which is characterized by a small number of mass parameters. For this purpose, we use so-called simplified models [31][32][33][34]. For gluino pair production, the T1tttt, T1bbbb, T1qqqq, and T5qqqqVV [35] simplified models are considered (Fig. 1). In the T1tttt model, each gluino undergoes a three-body decay g → tt χ 0 1 , where χ 0 1 is the LSP. The T1bbbb and T1qqqq models are the same as the T1tttt model, except the tt system is replaced by bottom quark-antiquark (bb) or light-flavored (u, d, s, c) quark-antiquark (qq) pairs, respectively. In the T5qqqqVV scenario, each gluino decays to a light-flavored qq pair and either to the next-to-lightest neutralino χ 0 2 or to the lightest chargino χ ± 1 . The probability for the decay to proceed via the χ 0 2 , χ + 1 , or χ − 1 is 1/3 for each channel. The χ 0 2 ( χ ± 1 ) subsequently decays to the χ 0 1 and to an on-or off-mass-shell Z (W ± ) boson. In this model, we assign For squark-antisquark production, three simplified models are considered, denoted T2tt, T2bb, and T2qq (Fig. 2). In the T2tt model, top squark-antisquark production is followed by the decay of the (anti)squark to a top (anti)quark and the χ 0 1 . The T2bb and T2qq models are the same as T2tt except with bottom squarks and quarks, or light-flavored squarks and quarks, respectively, in place of the top squarks and quarks.

Detector and trigger
A detailed description of the CMS detector, along with a definition of the coordinate system and pertinent kinematic variables, is given in Ref. [36]. 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 range |η| < 2.5, where η is the pseudorapidity. The ECAL and HCAL, each composed of a barrel and two endcap sections, cover |η| < 3.0. Forward calorimeters extend the coverage to 3.0 < |η| < 5.2. Muons are measured within |η| < 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 is described in Ref. [37]. 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 is measured in data and is found to exceed 97% for events satisfying the event selection criteria described below. Additional triggers requiring the presence of charged leptons, photons, or minimum values of H T are used to select control samples for the evaluation of backgrounds, as described below.

Event reconstruction
Individual particles are reconstructed with the CMS particle-flow (PF) algorithm [38], which identifies them as photons, charged hadrons, neutral hadrons, electrons, or muons. To improve the quality of the photon and electron reconstruction, additional criteria are imposed on the σ ηη variable [39], which is a measure of the width of the ECAL shower shape with respect to the η coordinate, and on the ratio of energies associated with the photon or electron candidate in the HCAL and ECAL [39,40]. For muon candidates [41], more stringent requirements are imposed on the matching between silicon tracker and muon detector track segments. Photon and electron candidates are restricted to |η| < 2.5 and muon candidates to |η| < 2.4.
The reconstructed vertex with the largest value of summed physics-object p 2 T is taken to be the primary pp interaction vertex, where the physics objects are the jets, clustered using the jet finding algorithm [42, 43] with the charged particle tracks assigned to the vertex as inputs, and the associated missing transverse momentum, taken as the negative vector sum of the p T of those jets. Charged particle tracks associated with vertices other than the primary vertex are removed from further consideration. 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.
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 ∆R = √ (∆φ) 2 + (∆η) 2 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 [44]. 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 [45]. The isolation requirement is I < 0.1 (0.2) for electrons (muons).
To further suppress leptons from hadron decays and also single-prong hadronic τ lepton decays, charged particle tracks not identified as an isolated electron or muon, including PF electrons and muons, are subjected to a track isolation requirement. (Note that PF electrons and muons that do not satisfy the isolation requirements of the previous paragraph are not considered to be electron and muon candidates in this analysis.) 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 |η| < 2.4.
Similarly, we require photon candidates to be isolated. The photon isolation requirement is based on the individual sums of energy from charged hadrons, neutral hadrons, and electromagnetic particles, excluding the photon candidate itself, within a cone of radius ∆R = 0.3 around the photon candidate's direction, corrected for pileup [39]. Each of the three individual sums is required to lie below a (different) threshold that depends on whether the photon appears in the barrel or endcap calorimeter.
Jets are defined by clustering PF candidates using the anti-k T jet algorithm [42, 43] with a distance parameter of 0.4. Jet quality criteria [46,47] are imposed to eliminate jets from spurious sources such as electronics noise. The jet energies are corrected for the nonlinear response of the detector [48] and to account for the expected contributions of neutral particles from pileup [44]. Jets are required to have p T > 30 GeV.
The identification of b jets (b jet tagging) is performed by applying, to the selected jet sample, a version of the combined secondary vertex algorithm based on deep neural networks (DeepCSV) [49]. The medium working point of this algorithm is used. The tagging efficiency for b jets with p T ≈ 30 GeV is 65%. The corresponding misidentification probability for gluon and up, down, and strange quark jets is 1.6% while that for charm quark jets is 13%.

Event selection and search regions
Events considered as signal candidates are required to satisfy: • no identified isolated electron or muon candidate with p T > 10 GeV; • 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 [50] formed from p miss T and the isolated-track p T vector, with p miss T the negative of the vector p T sum of all PF objects with appropriate calibration applied as explained in Ref. [51]; the m T requirement restricts the veto to situations consistent with a W boson decay; • no identified, isolated photon candidate with p T > 100 GeV; this requirement has a minimal impact on signal efficiency and is implemented to make the analysis orthogonal to SUSY searches based on events with photons and missing transverse energy, which typically require photon p T 100 GeV (e.g., Ref. [52]); • ∆φ H miss T ,j i > 0.5 for the two highest p T jets j 1 and j 2 , with ∆φ H miss T ,j i the azimuthal angle between H miss T and the p T vector of jet j i ; if N jet ≥ 3, then, in addition, ∆φ H miss T ,j 3 > 0.3 for the third-highest p T jet j 3 ; if N jet ≥ 4, then, yet in addition, ∆φ H miss T ,j 4 > 0.3 for the fourth-highest p T jet j 4 ; all considered jets must have |η| < 2.4; these requirements suppress background from QCD events, for which H miss T is usually aligned along a jet direction.
In addition, anomalous events with reconstruction failures or that arise from noise or beam halo interactions are removed [51].
For H T and H miss T , 10 kinematic intervals are defined, as indicated in Table 1 and Fig. 3. For N jet ≥ 8, the kinematic intervals labeled 1 and 4 are discarded because of the small numbers of events. The total number of search bins in the four-dimensional space is 174. >850 850-1700 10 >850 >1700

Simulated event samples
The evaluation of background (Section 6) is primarily based on data control regions. Samples of MC simulated SM events are used to evaluate multiplicative transfer factors that account for kinematic or other selection criteria differences between the data control and signal regions and to validate the analysis procedures.
The SM production of tt, W+jets, Z+jets, γ+jets, and QCD events is simulated using the MAD-GRAPH5 aMC@NLO 2.2.2 [53,54] event generator with leading order (LO) precision. The tt events are generated with up to three additional partons in the matrix element calculations. The W+jets, Z+jets, and γ+jets events are generated with up to four additional partons. Single top quark events produced through the s channel, diboson events such as those originating from WW, ZZ, or ZH production (with H a Higgs boson), and rare events such as those from ttW, ttZ, and WWZ production, are generated with MADGRAPH5 aMC@NLO 2.2.2 at next-toleading order (NLO) [55], except that WW events in which both W bosons decay leptonically are generated using the POWHEG v2.0 [56][57][58][59][60] program at NLO. This 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 [61] suite of programs. Normalization of the simulated background samples is performed using the most accurate cross section calculations available [53,59,60,[62][63][64][65][66][67][68][69][70], which generally correspond to NLO or next-to-NLO (NNLO) precision.
Samples of simulated signal events are generated at LO using MADGRAPH5 aMC@NLO 2.2.2, with up to two additional partons included in the matrix element calculations. The production cross sections are determined with approximate NNLO plus next-to-next-to-leading logarithmic (NNLL) accuracy [71][72][73][74][75]. Events with gluino (squark) pair production are generated for a range of gluino m g (squark m q ) and LSP m and m g , as was already stated in the introduction. The gluinos and squarks decay according to the phase space model [76]. To render the computational requirements manageable, the detector response is described using the CMS fast simulation program [77,78], which yields results that are generally consistent with the GEANT4-based simulation. To improve the consistency of the fast simulation description with respect to that based on GEANT4, we apply a correction of 1% to account for differences in the efficiency of the jet quality requirements [46, 47], 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 .
All simulated samples make use of the PYTHIA 8.205 [76] program to describe parton showering and hadronization. The CUETP8M1 [79] (CP5 [80]) PYTHIA 8.205 tune was used to produce the SM background samples for the analysis of the 2016 (2017 and 2018) data, with signal samples based on the CUETP8M1 tune for 2016 and on the CP2 tune [80] for 2017 and 2018. Simulated samples generated at LO (NLO) with the CUETP8M1 tune use the NNPDF2.3LO (NNPDF2.3NLO) [81] parton distribution function (PDF), while those using the CP2 or CP5 tune use the NNPDF3.1LO (NNPDF3.1NNLO) [82] PDF. The simulated events are generated with a distribution of pp interactions per bunch crossing that is adjusted to match the corresponding pileup distribution measured in data.
To improve the description of initial-state radiation (ISR), the MADGRAPH5 aMC@NLO prediction is compared 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 remaining jets in the event is denoted N ISR jet . A correction factor is applied to simulated tt and signal events so that the N ISR jet distribution agrees with that in data. The correction is found to be unnecessary for tt samples that are generated with the CP5 tune, so it is not applied to those samples. The central value of the correction ranges from 0.92 for N ISR jet = 1 to 0.51 for N ISR jet ≥ 6. 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 signal and tt event production.

Background evaluation
The evaluation of the SM backgrounds 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 accounted for in the interpretation of the results (Section 8). Signal contamination is negligible for all CRs except for the single-lepton CR described in Section 6.1. Similarly, it is negligible for all signal models except those that can produce an isolated track or lepton. With respect to the models examined here, signal contamination is relevant only for the T1tttt, T5qqqqVV, and T2tt models.

Background from top quark and W+jets events: "lost leptons"
The background from the SM production of tt, single top quark, and W+jets events originates from W bosons that decay leptonically to yield a neutrino and a charged lepton. The charged lepton can be an electron, a muon, or a τ lepton. The τ lepton can decay leptonically to produce an electron or muon or it can decay hadronically, in each case yielding at least one additional neutrino. For W boson decays that produce electrons or muons, top quark and W+jets events can enter as background to the signal region if there is large H miss T from the neutrino(s) and if the electron or muon lies outside the analysis acceptance, is not reconstructed, or is not isolated. For W boson decays that produce a hadronically decaying τ lepton, top quark and W+jets events can enter as background if there is large H miss T from the neutrinos. Collectively, the background from events with top quark and W+jets production is referred to in this paper as the "lost-lepton" background.
To evaluate the lost-lepton background, a single-lepton (e, µ) CR is selected using the same trigger and event selection criteria used for signal events, except the electron and muon vetoes are inverted and the isolated-track veto is not applied. Exactly one isolated electron or muon is required to be present. The single-electron and single-muon samples are combined to form a single CR. The transverse mass m T formed from p miss T and the lepton p T vector is required to satisfy m T < 100 GeV. This requirement has a high efficiency for SM events while reducing potential contamination from signal events with large p miss T . The signal contamination in the resulting CR is generally small, with a typical value of 7, 3, and 1% for the T1tttt, T5qqqqVV, and T2tt model, respectively. The contamination tends to be larger in search  The lost-lepton background is evaluated by applying an MC-derived multiplicative transfer factor to the observed single-lepton CR yields, with a separate transfer factor determined for each of the 174 search bins. The transfer factor is defined by the ratio, in simulation, of the number of lost-lepton events in a search bin to the number of events in the corresponding bin of the single-lepton CR, following normalization to the same integrated luminosity. The simulated events are corrected to account for differences with respect to data in the lepton, isolated track, and b jet tagging efficiencies.
The upper panel of Fig. 4 shows the simulated results, as a function of N jet and N b-jet , for the number of lost-lepton events. The corresponding results from simulation for the number of events in the single-lepton CR are shown in the middle panel of Fig. 4. The ratio of the results in the upper to the middle panels, equivalent to the transfer factor integrated over H T and H miss T , is shown in the lower panel. At lower values of N jet , the distributions are enhanced in W+jets events, for which a larger fraction of leptons lie outside the kinematic acceptance of the analysis compared to tt events. This reduces the event acceptance in the single-lepton CR, increasing the value of the integrated transfer factors above unity as seen in the lower panel of Fig. 4 for 2 ≤ N jet ≤ 3. As N b-jet increases, the probability for a lepton to fail the isolation requirement increases, leading to a larger rate of lost-lepton events and to an increase in the integrated transfer factors. This latter effect is especially visible for 2 ≤ N jet ≤ 3 in Fig. 4 (lower).
The dominant uncertainty in the lost-lepton background prediction is statistical, arising from the limited number of events in the CR. Other uncertainties are evaluated to account for the lepton and b jet tagging scale factors, the m T selection requirement, the PDFs, the renormalization and factorization scales [83], and the jet energy corrections. These uncertainties are summed in quadrature to obtain the total uncertainty in the lost-lepton background prediction.

Background from Z(→ νν )+jets events
The background from Z+jets events with Z → νν decay is evaluated using a CR with a single photon (γ+jets CR), in conjunction with a Z(→ + − )+jets CR in which the Z boson decays to an e + e − or µ + µ − pair. The method relies on the kinematic similarity between the production of Z bosons and photons. The Z(→ νν )+jets background in search bins with N b-jet = 0 is   determined by applying multiplicative transfer factors from simulation to the observed rate of γ+jets events, analogous to the method described in Section 6.1 for the evaluation of the lostlepton background. A correction is made to the normalization based on the observed rate of Z(→ + − )+jets CR events. An extrapolation to the search bins with N b-jet ≥ 1 is then made based on factors constructed from the Z(→ + − )+jets data. We follow this procedure in order to take advantage of both the higher statistical precision of the γ+jets CR and the more direct transfer factors of the Z → + − CR, while preserving the N b-jet -N jet correlation observed in the latter.

The γ+jets events
Events in the γ+jets CR were collected using a single-photon trigger, with an online threshold that varied between 180 and 190 GeV, depending on the data collection period. In the offline analysis, events are required to contain exactly one photon with p T > 200 GeV. In each CR event, the photon serves as a proxy for a Z boson and is removed to emulate the undetected Z boson in Z → νν decays. To ensure that the kinematics of the γ+jets events match those expected for Z(→ νν )+jets events, jets are reclustered after removing the photon and all eventlevel variables are recomputed. The same event selection criteria used to select signal events are then applied except, in addition, we require N b-jet = 0.
The γ+jets CR contains nonnegligible contributions from photons produced in neutral meson decays. These photons are referred to as "nonprompt." The contamination of the CR from nonprompt photons, and thus the purity of signal photons in the sample, is evaluated using a binned maximum likelihood fit to the distribution of the photon candidate's charged hadron isolation variable. The fit is based on templates for nonprompt and signal photons. For signal photons, the template is taken from simulation, using the nominal photon selection criteria. For nonprompt photons, three different versions of the template are made: i) from simulation using the nominal criteria; ii) from simulation in a high-σ ηη sideband (defined by inverting the σ ηη selection criterion), where nonprompt photon production is expected to dominate; and iii) from data in this same high-σ ηη sideband. The arithmetic mean of the three nonprompt templates is used in the fit, with the variation in the results obtained using the three templates individually defining a systematic uncertainty. The purity is determined as a function of H miss T and typically exceeds 90%.
In the generation of simulated γ+jets events, photons that are approximately collinear with a parton (∆R < 0.4) are removed to improve the fraction of events with well-isolated photons and thus the statistical precision of the sample. A correction denoted F dir is evaluated to account for a bias from this requirement, using simulated events with a looser restriction on the angular separation between the generator-level photons and partons. The corrections are typically less than 10%. A systematic uncertainty in the correction given by 0.30(1 − F dir ) is determined by evaluating the level of agreement between simulation and data in the distribution of the angular separation between a photon and the nearest jet, and the effect of changing the definition of collinear photons in the simulation.

The Z(→ + − )+jets events
The Z(→ + − )+jets CR, collected using single-lepton triggers, is selected by requiring two oppositely charged electrons or muons with a dilepton invariant mass m within 15 GeV of the Z boson mass. The selection requirements for electrons and muons are the same as those described in Section 3, including the isolation requirements. To suppress tt events, the p T of the dilepton system is required to exceed 200 GeV. Similar to the γ+jets CR, the lepton pair in each Z(→ + − )+jets event is removed to emulate the undetected Z boson in Z(→ νν )+jets events, following which jets are reclustered and the event-level quantities recalculated.
Top quark pair production typically constitutes <5% of the observed dilepton event yield, except for events with N b-jet ≥ 2 where it can comprise up to ≈15% of the sample. Using fits to the observed m distribution, the purity β data of the Z(→ + − )+jets sample is evaluated for each individual N jet and N b-jet region.

The Z(→ νν )+jets background prediction
For each of the 46 search bins with N b-jet = 0, the Z(→ νν )+jets background is evaluated according to: where N data γ is the number of observed events in the γ+jets CR, R sim Z→νν /γ is the transfer factor, C γ data/sim accounts for the trigger efficiency and for differences between data and simulation in the photon reconstruction efficiency [39], and β γ is the photon purity. The transfer factors, which account for known differences between photon and Z boson production, are given by the ratio from simulation of the rates of Z(→ νν )+jets events to γ+jets events in the 46 bins. For the photon selection criteria used in this analysis, the transfer factor has a value of around 0.5, with a relatively mild dependence on the signal region kinematics. The distribution of N data γ , along with the simulated results for signal and nonprompt γ+jets events, is shown in Fig. 5 (upper). Figure 5 (lower) shows the transfer factors R sim Z→νν /γ .
The term denoted ρ in Eq. (1) accounts for possible residual mismodeling of R sim Z→νν /γ . The value of ρ is expected to be close to unity, with possible deviations due to differences in missing higher-order terms between the γ+jets and Z+jets simulation. It is the average over all search bins with N b-jet = 0 of the double ratio where N data Z→ + − and N sim Z→ + − represent the number of events in the observed and simulated Z → + − CR, respectively, N sim γ is the number of events in the simulated γ+jets CR, and C data/sim accounts for the trigger efficiency and for differences between data and simulation in the lepton reconstruction efficiencies in Z(→ + − )+jets events [40,41]. The event yields in the Z(→ + − )+jets CR are too small to allow a meaningful determination of ρ in all search bins and thus we calculate the average ρ and apply it to all bins.
From studies of the variation of ρ with H T , H miss T , and N jet , we observe a mild trend in ρ with respect to H T . This trend is parameterized as ρ(H T ) = 0.86 + (2.0 × 10 −4 )min(H T , 900 GeV). Using this parameterization, an event-by-event weight is applied to each simulated γ+jets CR event before it enters Eq. (1). Prior to this event weighting, we find ρ = 0.95. Following the event weighting, ρ = 1.00. It is this latter value of ρ , along with its uncertainty, that enters Eq. (1). In each bin, the residual deviation of ρ from unity as a function of H T is added in quadrature with the associated statistical uncertainty, and analogously but separately for H miss T and N jet , and the largest of the three resulting terms is taken as the corresponding systematic uncertainty in the background prediction. The values of this bin-dependent uncertainty range from 1 to 13%.
To evaluate the Z(→ νν )+jets background for search bins with N b-jet ≥ 1, we assume that the relative population of Z(→ νν )+jets events in the H T -H miss T plane is independent of N b-jet for fixed N jet . A systematic uncertainty deduced from a closure test (described below) is assigned to account for this assumption, where "closure test" refers to a check of the ability of the method, applied to simulated event samples, to correctly predict the genuine number of background events in simulation. We extend the result from Eq.  Table 1 and Fig. 3. The uncertainties are statistical only. For the upper plot, the simulated results show the stacked event rates for the γ+jets and nonprompt MC event samples, where "nonprompt" refers to SM MC events other than γ+jets. The simulated nonprompt results are dominated by events from the QCD sample. Because of limited statistical precision in the simulated event samples at large N jet , the transfer factors determined for the 8 ≤ N jet ≤ 9 region are also used for the N jet > 10 region.
F data j,b from Z(→ + − )+jets data, as follows: where j corresponds to the five N jet regions, b to the four N b-jet regions (three for N jet ≤ 3), and k to the 10 kinematic regions of H T and H miss T (   The rare process ttZ and the even more rare processes ZZ, WWZ, WZZ, and ZZZ can also contribute to the background. Those processes with a counterpart when the Z boson is replaced with a photon are already accounted for in N data γ and thus are automatically included in the background estimate. We assume that the ratio of the rate of the rare process to its counterpart with a photon, e.g., the ratio of ttZ (with Z → νν ) to tt γ events, equals R sim Z→νν /γ .
A closure test of the procedure is performed by treating event yields from the Z(→ + − )+jets simulation as data, as shown in Fig. 7. Based on this study, the following systematic uncertainties are assigned. For N jet = 2-3, a systematic uncertainty of 15 and 30% is assigned to the N b-jet = 1 and ≥2 regions, respectively. For N jet ≥ 4, a systematic uncertainty of 15 and 30% is assigned to the N b-jet = 1-2 and ≥3 regions. These uncertainties account for correlations between N b-jet and the H T and/or H miss T variables in the shape of the Z → νν prediction.

Background from QCD events
The QCD background comprises only a small fraction (<5%) of the total background but, because it typically arises from the mismeasurement of jet p T , is difficult to evaluate with simula-   Table 1 and Fig. 3. For bins with N jet ≥ 10, some points do not appear in the upper panel because they lie below the minimum of the displayed range. In the case that the direct expected yield is zero, there is no result in the lower, ratio panel. The pink bands show the statistical uncertainties in the prediction, scaled to correspond to the integrated luminosity of the data, combined with the systematic uncertainty attributable to the kinematic (H T and H miss T ) dependence. The black error bars show the statistical uncertainties in the simulation. For bins corresponding to N b-jet = 0, the agreement is exact by construction.

fb Simulation
tion. We use data to model this background, exploiting knowledge of the jet energy resolution. Briefly, the method employs a set of CR events collected using triggers requiring H T to exceed various thresholds between 200 and 1050 GeV, with no condition on H miss T . Corresponding prescale factors ranging from around 10 000 to 1 are applied, where a prescale factor reduces the recorded event rate relative to the raw trigger rate in order to maintain a manageable data flow. The jet momenta in each CR event are adjusted so that the event has well-balanced jet p T , consistent with the kinematics of a generator-level (i.e., ideally measured) QCD event. This step is called rebalancing. The rebalancing step removes the intrinsic p miss T from the event, thus effectively eliminating the contributions of events like W+jets and Z+jets events that can have genuine p miss T [29]. The jet momenta are then smeared according to the known detector jet p T resolution in order to determine the probability that a given event will populate a given search bin. This latter step is the smear stage. The so-called rebalance and smear (R&S) method was introduced in Refs. [29,30] and was further developed in Ref. [3].
To rebalance an event, a Bayesian inference procedure is used, in which the p T of each jet in a CR event is varied within its uncertainty to maximize the probability: where P ( J true | J meas ) is the posterior probability density for a given configuration of jets with true (or ideal) momentum assignments J true , given a configuration of measured jet momenta J meas . The P ( J meas | J true ) term, taken to be the product of the individual jet response functions of all jets in an event, is the likelihood to observe a configuration of measured jet momenta given a configuration of jets with a particular set of true momenta. The jet response functions are constructed from the distributions in simulation of the ratio of the reconstructed jet p T to the p T of well-matched generator-level jets. The response functions are derived as a function of jet p T and η and are corrected to account for differences in the jet response shape between data and simulation. The π( H miss T,true , ∆φ j 1(b) ,true ) term is the prior distribution, determined as a function of the true (i.e., generator level) H miss T and ∆φ j 1(b) , where ∆φ j 1(b) is the azimuthal angle between H miss T and either the highest p T jet in the event (for N b-jet = 0), or the highest p T tagged b jet (for N b-jet ≥ 1). This prior represents the distribution of the magnitude and direction of the genuine H miss T expected in QCD events.
After the transverse momenta of the individual jets have been adjusted according to the posterior probability density in Eq. (4), the jet p T values are smeared by rescaling them using factors sampled randomly from the jet response functions. This sampling is performed numerous times for each rebalanced event. Each event is then weighted by the inverse of the number of times it is smeared. Events are smeared in up to 1000 independent trials, with a final target event weight of 0.05, equal to the prescale value of the trigger that collected the seed event divided by the number of times the event was reused in the smearing step.
The R&S procedure produces a sample of events that closely resembles the original sample of CR events, except with the contributions of the electroweak backgrounds effectively removed. The resulting events are subjected to the signal event selection criteria of Section 4 to obtain the QCD background prediction in each search bin. The overall normalization is adjusted based on a scaling factor derived from a QCD-dominated CR selected by inverting the ∆φ selection criteria and requiring N b-jet = 0 and 250 < H miss T < 300 GeV. The ∆φ selection criteria are inverted by requiring at least one of the two (for N jet = 2), three (for N jet = 3), or four (for N jet ≥ 4) highest p T jets in an event to fail at least one of the corresponding ∆φ H miss  Figure 9 shows the observed and predicted event yields in 174 analysis control bins defined using the same criteria as for the search bins except with the inverted-∆φ requirement. For all these validation tests, contributions from QCD events are evaluated using the R&S method, contributions from top quarks and W+jets events are evaluated using the lost-lepton method described in Section 6.1, and contributions from Z(→ νν )+jets events are taken from simulation.
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 30-70%, depending on the search bin. Smaller uncertainties related to the trigger and the finite size of the seed sample are evaluated, as well as a nonclosure uncertainty that accounts for inaccuracies identified from simulation-based studies.

Signal systematic uncertainties
Systematic uncertainties in the signal event yield are listed in Table 2. 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 [83][84][85]. The uncertainties associated with µ R , µ F , and ISR, integrated over all search bins, typically lie below 0.1%. Nonetheless, they can be as large as the maximum values noted in Table 2 if ∆m ≈ 0, where ∆m is the difference between the gluino or squark mass and the sum of the masses of the particles into which the gluino or squark decays. For example, for the T1tttt model, ∆m = m g − (m To evaluate the uncertainty associated with the pileup reweighting, the value of the total inelastic cross section is varied by 5% [86]. The isolated-lepton 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 varies between 2.3 and 2.5% [87][88][89], depending on the year of data collection.
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   Fig. 7. The lower panel shows the ratio of the observed to the predicted event yields, with their statistical uncertainties. The hatched region indicates the total uncertainty in the prediction, with statistical and systematic uncertainties combined in quadrature. account for these potential changes in shape, i.e., migration of events among search bins, in the limit setting procedure described in Section 8. Figure 10 presents the observed numbers of events in the 174 search bins. The data are shown in comparison to the stacked pre-fit predictions for the SM backgrounds, where "pre-fit" refers to the predictions determined as described in Section 6, before constraints from the fitting procedure have been applied. Numerical values are given in Appendix A. The uncertainties in the background predictions are mainly from systematic uncertainties in the transfer factors, statistical uncertainties in control sample yields, and systematic uncertainties in the modeling of the search variables. Appendix A lists the overall statistical and systematic uncertainties for the individual background components and for their sum. In addition to the finely segmented search bins of Fig. 10, we determine the results for 12 aggregate search bins, each representing a potentially interesting signal topology. These results are presented in Appendix B.

Results
The observed event counts are consistent with the predicted backgrounds. Thus we do not obtain evidence for supersymmetry. Figure 11 presents one-dimensional projections of the data and SM predictions in H miss T , N jet , and N b-jet . Additional projections are shown in Fig. 12. For these latter results, criteria have been imposed, as indicated in the legends, to enhance the sensitivity for a particular signal process. For both Figs. 11 and 12, two example signal distributions are shown: one with ∆m 0 and one with ∆m ≈ 0, where both example scenarios lie well within the parameter space excluded by the present study. The notation ∆m 0 means that the mass difference ∆m is large compared to the sum of the masses of the particles into which the gluino or squark decays.
Upper limits are evaluated for the production cross sections of the signal scenarios using a likelihood fit. The SUSY signal strength µ, defined by the ratio of cross sections µ ≡ σ SUSY /σ SM , the signal uncertainties described in Section 7, the predicted SM background contributions shown in Fig. 10, the uncertainties in these backgrounds listed in Appendix A, and the control sample yields are all inputs to the fit. The background uncertainties, uncertainties in the signal shape and normalization, and control sample statistical uncertainties are assigned as nuisance parameters, which are constrained in the fit.
For the models of gluino (squark) pair production, the limits are derived as a function of m g (m q ) and m . The test statistic is q µ = −2 ln(L µ /L max ), 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 likelihood for a fixed signal strength. Limits are set under the asymptotic approximation [90], with q µ approximated with an Asimov data set and used in conjunction with the CL s criterion described in Refs. [91,92].
We evaluate 95% confidence level (CL) upper limits on the signal cross sections. The approximate NNLO+NNLL cross section is used to determine corresponding exclusion curves. Before computing these limits, the signal yields are corrected to account for the predicted signal contamination in the CRs from the signal model under consideration. Beyond the observed exclusion limits, we derive expected exclusion limits by evaluating the test statistic using the predicted numbers of background events with their expected Poisson fluctuations.  In addition to the main T2qq model, with four mass-degenerate squark flavors (up, down, strange, and charm), each arising from two different quark spin states, Fig. 14 (lower) shows the results should only one of these eight states ("Single q") be accessible at the LHC. In this case, the upper limit on the squark mass is reduced to 1130 GeV.    The results are interpreted in the context of simplified models for gluino and squark pair production. For the gluino models, each of the produced gluinos decays either to a tt pair and an undetected, stable, lightest supersymmetric particle, assumed to be the χ 0 1 neutralino (T1tttt model); to a bb pair and the χ 0 1 (T1bbbb model); to a light-flavored (u, d, s, c) qq pair and the χ 0 1 (T1qqqq model); or to a light-flavored quark and antiquark and either the second-lightest neutralino χ 0 2 or the lightest chargino χ ± 1 , followed by decay of the χ 0 2 ( χ ± 1 ) to the χ 0 1 and an on-or off-mass-shell Z (W ± ) boson (T5qqqqVV model). For the squark models, each of the

95% CL upper limit on cross section [pb]
produced squarks decays either to a top quark and the χ 0 1 (T2tt model), to a bottom quark and the χ 0 1 (T2bb model), or to a light-flavored quark and the χ 0 1 (T2qq model). Using the predicted cross sections with next-to-leading order plus approximate next-to-leading logarithm accuracy as a reference, gluinos with masses as large as from 2000 to 2310 GeV are excluded at 95% confidence level, depending on the signal model. The corresponding limits on the masses of directly produced squarks range from 1190 for top squarks to 1630 GeV for light-flavored squarks. The results presented here supersede those of Ref.
[7], extending the mass limits of this previous study by, typically, 200 GeV or more.

Acknowledgments
We congratulate our colleagues in the CERN accelerator departments for the excellent performance of the LHC and thank the technical and administrative staffs at CERN and at other CMS institutes for their contributions to the success of the CMS effort. In addition, we gratefully acknowledge the computing 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:       [46] CMS Collaboration, "Jet performance in pp collisions at √ s = 7 TeV", CMS Physics Analysis Summary CMS-PAS-JME-10-003, 2010.

A Numerical results for the full set of search bins
In this appendix, we present numerical values for the results in the 174 search bins shown in Fig. 10. Table 3: Observed number of events and pre-fit background predictions in the 2 ≤ N jet ≤ 3 search bins. For the background predictions, the first uncertainty is statistical and the second systematic. Bin [GeV] background background background background

B Aggregate search bins
To simplify the results from the full set of search bins, we present in this appendix the observed number of events and corresponding SM background prediction in 12 aggregate search bins, obtained by summing the results from the nominal search bins while taking correlations into account. The aggregate bins are intended to represent 12 general topologies of interest, as indicated in Table 8. The intervals used to define the aggregate bins are optimized using the signal models described in this paper. The definitions of the aggregate bins, along with the corresponding background predictions and observed event counts, are given in Table 9. The corresponding data are presented in Fig. 15.    Figure 15: The observed numbers of events and pre-fit SM background predictions in the aggregate search bins. The total background uncertainty is shown by the hatched regions. The lower panel displays the fractional differences between the data and the SM predictions.