Inclusive search for supersymmetry in pp collisions at $\sqrt{s} =$ 13 TeV using razor variables and boosted object identification in zero and one lepton final states

An inclusive search for supersymmetry (SUSY) using the razor variables is performed using a data sample of proton-proton collisions corresponding to an integrated luminosity of 35.9 fb$^{-1}$, collected with the CMS experiment in 2016 at a center-of-mass energy of $\sqrt{s} =$ 13 TeV. The search looks for an excess of events with large transverse energy, large jet multiplicity, and large missing transverse momentum. The razor kinematic variables are sensitive to large mass differences between the parent particle and the invisible particles of a decay chain and help to identify the presence of SUSY particles. The search covers final states with zero or one charged lepton and features event categories divided according to the presence of a high transverse momentum hadronically decaying W boson or top quark, the number of jets, the number of b-tagged jets, and the values of the razor kinematic variables, in order to separate signal from background for a broad range of SUSY signatures. The addition of the boosted W boson and top quark categories within the analysis further increases the sensitivity of the search, particularly to signal models with large mass splitting between the produced gluino or squark and the lightest SUSY particle. The analysis is interpreted using simplified models of $R$-parity conserving SUSY, focusing on gluino pair production and top squark pair production. Limits on the gluino mass extend to 2.0 TeV, while limits on top squark mass reach 1.14 TeV.

The search described in this paper is an extension of previous work presented in Refs. [2,3]. The search is inclusive in scope, covering final states with zero or one charged lepton. To enhance sensitivity to specific types of SUSY signatures, the events are categorized according to the presence of jets consistent with high transverse momentum (p T ) hadronically decaying W bosons or top quarks, the number of identified charged leptons, the number of jets, and the number of b-tagged jets. The search is performed in bins of the razor variables M R and R 2 [1][2][3]. The result presented in this paper is the first search for SUSY from the CMS experiment that incorporates both Lorentz-boosted and "nonboosted" (resolved) event categories. This search strategy provides broad sensitivity to gluino and squark pair production in R-parity [27] conserving scenarios for a large variety of decay modes and branching fractions. The prediction of the SM background in the search regions (SRs) is obtained from Monte Carlo (MC) simulation calibrated with data control regions (CRs) that isolate the major background components. Additional validation of the assumptions made by the background estimation method yields estimates of the systematic uncertainties.
Other searches for SUSY by the CMS [28-36] and ATLAS [37-43] Collaborations have been performed using similar data sets and yield complementary sensitivity. Compared to those searches, the razor kinematic variables explore alternative signal-sensitive phase space and add robustness to the understanding of the background composition and the potential systematic uncertainties in the background models. To give a characteristic example, for squark pair production with a squark mass of 1000 GeV and a neutralino mass of 100 GeV, we find that the overlap of signal events falling in the most sensitive tail regions of the razor kinematic variables and of other kinematic variables used in alternative searches described in Ref.
We present interpretations of the results in terms of production cross section limits for several simplified models [44][45][46][47] for which this search has enhanced sensitivity. The simplified models considered include gluino pair production, with each gluino decaying to a pair of top quarks and the lightest SUSY particle (LSP), referred to as "T1tttt"; gluino pair-production, with each gluino decaying to a top quark and a low-mass top squark that subsequently decays to a charm quark and the LSP, referred to as "T5ttcc"; and top squark pair production, with each top squark decaying to a top quark and the LSP, referred to as "T2tt". The corresponding diagrams for these simplified models are shown in Fig. 1. Although we only interpret the search results in a limited set of simplified models, the search can be sensitive to other simplified models that are not explicitly considered in this paper. This paper is organized as follows. Details of the detector, trigger, and object reconstruction and identification are described in Section 2. The MC simulation samples used to model background and signal processes are described in Section 3. The analysis strategy and event categorization are discussed in Section 4, and the background modeling is discussed in Section 5. Systematic uncertainties are discussed in Section 6, and finally the results and interpretations are presented in Section 7. We summarize the paper in Section 8.  Figure 1: Diagrams for the simplified models considered in this analysis: (left) pair-produced gluinos, each decaying to two top quarks and the LSP, denoted T1tttt; (middle) pair-produced gluinos, each decaying to a top quark and a low mass top squark that subsequently decays to a charm quark and the LSP, denoted T5ttcc; (right) pair-produced top squarks, each decaying to a top quark and the LSP, denoted T2tt. In the diagrams, the gluino is denoted by g, the top squark is denoted by t, and the lightest neutralino is denoted by χ 0 1 and is the LSP.

The CMS detector and object reconstruction
The CMS detector consists of a superconducting solenoid of 6 m internal diameter, providing a magnetic field of 3.8 T. Within the solenoid volume there are a silicon pixel and a silicon strip tracker, a lead tungstate crystal electromagnetic calorimeter (ECAL), and a brass and scintillator hadron calorimeter (HCAL), each composed of a barrel and two endcap sections. Extensive forward calorimetry complements the coverage provided by the barrel and endcap detectors. Muons are measured in gas-ionization detectors embedded in the magnet steel flux-return yoke outside the solenoid. Events are selected by a two-level trigger system. The first level is based on a hardware filter, and the second level, the high level trigger, is implemented in software. A more detailed description of the CMS detector, together with a definition of the coordinate system used and the relevant kinematic variables, can be found in Ref. [48].
Physics objects are defined using the particle-flow (PF) algorithm [49], which aims to reconstruct and identify each individual particle in an event using an optimized combination of information from the various elements of the CMS detector. Jets are clustered from PF candidates using the anti-k T algorithm [50,51] with a distance parameter of 0.4. Jet energy corrections are derived from simulation and confirmed by in-situ measurements of the energy balance in dijet, multijet, photon+jet, and leptonically decaying Z+jet events [52]. Further details of the performance of the jet reconstruction can be found in Ref. [53]. Jets used in any selection of this analysis are required to have p T > 30 GeV and pseudorapidity |η| < 2.4. To identify jets originating from b quarks, we use the "medium" working point of the combined secondary vertex (CSVv2) b jet tagger, which uses an inclusive vertex finder to select b jets [54]. The efficiency to identify a bottom jet is in the range of 50-65% for jets with p T between 20 and 400 GeV, while the misidentification rate for light-flavor quark and gluon jets (charm jets) is about 1 (10)%. We also use the "loose" working point of the CSVv2 b jet tagger to identify b jets to be vetoed in the definition of various CRs. The loose b jet tagging working point has an efficiency of 80% and a misidentification rate for light-flavor and gluon jets of 10%. s Large-radius jets used for identifying Lorentz-boosted W bosons and top quarks are clustered using the anti-k T algorithm with a distance parameter of 0.8. The subset of these jets having |η| < 2.4 and p T > 200 (400) GeV are used to identify W bosons (top quarks). Identification is done using jet mass, the N-subjettiness variables [55], and subjet b tagging for top quarks. Jet mass is computed using the soft-drop algorithm [56], and is required to be between 65-105 and 105-210 GeV for W bosons and top quarks, respectively. The N-subjettiness variables: k p T,k min (∆R 1,k , ∆R 2,k , · · · , ∆R N,k ) , where N denotes candidate axes for subjets, k runs over all constituent particles, and d 0 = R 0 ∑ k p T,k . R 0 is the clustering parameter of the original jet, and ∆R n,k is the distance from constituent particle k to subjet n. The N-subjettiness variable is used to evaluate the consistency of a jet with having N subjets. To enhance discrimination, the ratios τ 21 = τ 2 /τ 1 and τ 32 = τ 3 /τ 2 are used for the W boson and top quark tagging, respectively, with the criteria of τ 21 < 0.40 and τ 32 < 0.65. For tagging top quarks ("t tagging"), an additional requirement is imposed on the subjet b tagging discriminant based on the multivariate CSVv2 algorithm [54]. The efficiencies for W boson and top quark tagging are on average 66 and 15%, respectively, with mistagging rates of 4.0 and 0.1% [53].
The missing transverse momentum vector p miss T is defined as the projection of the negative vector sum of the momenta of all reconstructed PF candidates on the plane perpendicular to the beams. Its magnitude is referred to as p miss T . Events containing signatures consistent with beam-induced background or anomalous noise in the calorimeters sometimes results in events with anomalously large values of p miss T and are rejected using dedicated filters [57,58]. The performance of the p miss T at CMS may be found in Ref. [59].
Electrons are reconstructed by associating an energy cluster in the ECAL with a reconstructed track [60], and are identified on the basis of the electromagnetic shower shape, the ratio of energies deposited in the ECAL and HCAL, the geometric matching of the track and the calorimeter cluster, the track quality and impact parameter, and isolation. To improve the efficiency for models that produce a large number of jets, a so-called "mini-isolation" technique is used, where the isolation cone shrinks as the momentum of the object increases. Further details are discussed in Ref. [2]. Muons are reconstructed by combining tracks found in the muon system with corresponding tracks in the silicon tracking detectors [61], and are identified based on the quality of the track fit, the number of detector hits used in the tracking algorithm, the compatibility between track segments, and isolation. Two types of selections are defined for electrons and muons: a "tight" selection with an average efficiency of about 70-75%, and a "veto" selection with an efficiency of about 90-95%. The veto selections are required to have p T > 5 GeV, while the tight selections are required to have p T > 30 and 25 GeV for electrons and muons, respectively. Similarly electrons (muons) are required to have |η| < 2.5 (2.4), and electrons with |η| (of 1.442-1.556) in the transition region between the barrel and endcap ECAL are not considered because of limited electron reconstruction capabilities in that region.
Hadronically decaying τ leptons (τ h ) are reconstructed using the hadron-plus-strips algorithm [62], which identifies τ lepton decay modes with one charged hadron and up to two neutral pions or three charged hadrons, and are required to be isolated. The "loose" selection used successfully reconstructs τ h decays with an efficiency of about 50%. The reconstructed τ h leptons have p T > 20 GeV and |η| < 2.4.
Finally, photon candidates are reconstructed from energy clusters in the ECAL [63] and identified based on the transverse shower width, the hadronic to electromagnetic energy ratio in the HCAL and ECAL, and isolation. Photon candidates that share the same energy cluster as an identified electron are vetoed. Photons are used in the estimation of Z → νν+jets backgrounds, and are required to have |η| < 2.5 and p T > 185 or 80 GeV for the nonboosted or boosted categories, respectively.

Simulation
Monte Carlo simulated samples are used to predict the SM backgrounds in the SRs and to calculate the selection efficiencies for SUSY signal models. Events corresponding to the Z+jets, γ+jets, and quantum chromodynamics (QCD) multijet background processes, as well as the SUSY signal processes, are generated at leading order with MADGRAPH5 aMC@NLO 2.2.2 [64,65] interfaced with PYTHIA V8.205 [66] for fragmentation and parton showering, and matched to the matrix element kinematic configuration using the MLM algorithm [67,68]. The CUETP8M1 PYTHIA 8 tune [69] was used. Other background processes are generated at nextto-leading order (NLO) with MADGRAPH5 aMC@NLO 2.2.2 [65] (W+jets, s-channel single top quark, ttW, ttZ processes) or with POWHEG v2.0 [70][71][72] (tt+jets, t-channel single top quark, and tW production), both interfaced with PYTHIA V8.205. Simulated samples generated at LO (NLO) used the NNPDF3.0LO (NNPDF3.0NLO) [73] parton distribution functions. The SM background events are simulated using a GEANT4-based model [74] of the CMS detector, while SUSY signal events are simulated using the CMS fast simulation package [75]. All simulated events include the effects of pileup, multiple pp collisions within the same or neighboring bunch crossings.
The SUSY particle production cross sections are calculated to NLO plus next-to-leading-log (NLL) precision [76][77][78][79][80][81] with all other sparticles assumed to be heavy and decoupled. The NLO+NLL cross sections and their associated uncertainties from Ref. [81] are taken as a reference to derive the exclusion limit on the SUSY particle masses.
To improve on the MADGRAPH5 aMC@NLO modeling of the multiplicity of additional jets from initial-state radiation (ISR), strongly produced SUSY signal samples are reweighted as a function of the number of ISR jets (N ISR jets ). This correction is derived from a tt enriched control sample such that the jet multiplicity from the MADGRAPH5 aMC@NLO-generated tt sample agrees with data. The reweighting factors vary between 0.92 and 0.51 for N ISR jets between one and six. We take one half of the deviation from unity as the systematic uncertainty in these reweighting factors.

Analysis strategy and event categorization
We perform the search in several event categories defined according to the presence of jets tagged as originating from a boosted hadronic W boson or top quark, the number of identified charged leptons, jets, and b-tagged jets. A summary of the categories used is shown in Table 1 below.
Events in the one-lepton category are required to have one and only one charged lepton (electron or muon), with p T above 30 (25) GeV for electrons (muons) selected using the tight criteria, while events in the zero-lepton category are required to have no electrons or muons passing the veto selection criteria and no τ h candidates. One-lepton events are placed in the "Lepton Multijet" category if they have between 4 and 6 jets, and placed in the "Lepton Seven-jet" category if they have 7 or more jets. One-lepton events with fewer than 4 jets are not considered in the analysis.
Zero-lepton events with jets tagged as originating from a boosted hadronic W boson or top quark decay are placed in a dedicated "boosted" event category. Events in this "boosted" category are analyzed separately with a set of CRs and validation tests specific for the analysis with boosted objects. They are further classified into those having at least one tagged W boson and one tagged b jet ("W" category), and those having at least one tagged top quark ("Top" category). Events in the W category are further divided into subcategories with 4-5 jets, and 6 jets or more. Zero-lepton events not tagged as having boosted W bosons or top quarks are placed into the "Dijet" category if they have two or three jets, the "Multijet" category if they have between 4 and 6 jets, and into the "Seven-jet" category if they have 7 or more jets. The Dijet category is further divided into subcategories with zero, one, and two or more btagged jets, and all other nonboosted categories are divided into subcategories with zero, one, two, and three or more b-tagged jets.
For each event in the above categories, we group the selected charged leptons and jets in the event into two distinct hemispheres called megajets, whose four-momenta are defined as the vector sum of the four-momenta of the physics objects in each hemisphere. The clustering algorithm selects the grouping that minimizes the sum of the squared invariant masses of the two megajets [82]. We define the razor variables M R and M R T as: where p j i , p j i T , and p j i z are the momentum of the ith megajet, its transverse component with respect to the beam axis, and its longitudinal component, respectively. The dimensionless variable R is defined as: For pair-produced SUSY signals, the variable M R quantifies the mass splitting between the pair-produced particle and the LSP, and exhibits a peaking structure, while for background it is distributed as an exponentially decaying spectrum. The variable R quantifies the degree of imbalance between the visible and invisible decay products and helps to suppress backgrounds which do not produce any weakly interacting particles. The combination of the two variables provide powerful discrimination between the SUSY signal and SM backgrounds.
Single-electron or single-muon triggers are used to collect events in the one-lepton categories, with a total trigger efficiency of about 80% for p T around 30 GeV, growing to 95% for p T above 50 GeV. Events in the boosted category are collected using triggers that select events based on the p T of the leading jet and the scalar p T sum of all jets, H T . The trigger efficiency is about 50% at the low range of the M R and R 2 kinematic variables and grows to 100% for M R > 1.2 TeV and R 2 > 0. 16. For the zero-lepton nonboosted event categories, dedicated triggers requiring at least two jets with p T > 80 GeV and loose thresholds on the razor variables M R and R 2 are used to collect the events. The trigger efficiency ranges from 95-100% and increases with M R and R 2 .
Preselection requirements on the M R and R 2 variables are made depending on the event category. For events in the one-lepton categories, further requirements are made on the transverse mass m T defined as follows: where p T is the charged-lepton transverse momentum, and ∆φ is the azimuthal angle (in radians) between the charged-lepton momentum and the p miss T . For events in the zero-lepton categories, further requirements are made on the azimuthal angle ∆φ R between the axes of the two razor megajets. These requirements are summarized in Table 2.
Finally, in each event category, the search is performed in bins of the kinematic variables M R and R 2 in order to take advantage of the varying signal-to-background ratio in the different bins. For one-lepton categories, the SRs are composed of five bins in M R , starting from 550 GeV, Hadronic razor and five bins in R 2 starting from 0.20. For the zero-lepton boosted categories, the SRs are composed of five bins in M R , starting from 800 GeV, and five bins in R 2 , starting from 0.08. Finally, for the zero-lepton nonboosted categories, the SRs are composed of five bins in M R , starting from 650 GeV, and four bins in R 2 starting from 0.30. To match with the expected resolution, the bin widths in M R increases from 100 to 300 GeV as the value of M R grows from 400 to 1200 GeV. In each category, bins are merged such that the expected background in each bin is larger than about 0.1 events. As a result, the SRs have a decreasing number of bins as the number of jets, b-tagged jets, and M R increases.

Background modeling
The main background processes in the SRs considered are W( ν)+jets (with = e, µ, τ), Z(νν)+jets, tt, and QCD multijet production. For event categories with zero b-tagged jets, the background is primarily composed of the W( ν)+jets and Z(νν)+jets processes, while for categories with two or more b-tagged jets it is dominated by the tt process. There are also small contributions at the level of a few percent from single top quark production, production of two or three electroweak bosons, and production of tt in association with a W or Z boson.
The background prediction strategy relies on the use of CRs to isolate each background process, address any deficiencies of the MC simulation using control samples in data, and estimate systematic uncertainties in the expected event yields. The CRs are defined such that they have no overlap with any SRs. For the dominant backgrounds discussed above, the primary sources of mismodeling come from inaccuracy in the MC prediction of the hadronic recoil spectrum and the jet multiplicity. Corrections to the MC simulation are applied in bins of M R , R 2 , and the number of jets (N jets ) to address these modeling inaccuracies. The CR bins generally follow the bins of the SRs described in Section 4, but bins with limited statistical power are merged in order to avoid large statistical fluctuations in the background predictions.
For the boosted categories, the CR selection and categorization are slightly adapted and the details are discussed further in Section 5.4. An additional validation of the background prediction method is also performed for the boosted categories.
In what follows, all background MC samples are corrected for known mismodeling of the jet energy response, the trigger efficiency, and the selection efficiency of electrons, muons, and b-tagged jets. These corrections are mostly in the range of 0-5%, but can be as large as 10% in bins with large M R and R 2 , where the corrections have larger statistical uncertainties.

The tt and W( ν)+jets backgrounds
We predict the tt and W( ν) backgrounds from the MC simulation corrected for inaccuracies in the modeling of the hadronic recoil. The corrections are derived in a CR consisting of events having at least one tight electron or muon. In order to separate the CR from the SRs and to reduce the QCD multijet background, the p miss T is required to be larger than 30 GeV, and m T is required to be between 30 and 100 GeV.
The one-lepton control sample is separated into W( ν)+jets-enriched and tt-enriched samples by requiring events to have zero (for W( ν)+jets), or one or more (for tt) b-tagged jets, respectively. The purity of the W( ν)+jets and tt dominated CRs are both about 80%. In each sample, corrections to the MC prediction are derived in two-dimensional bins in M R and R 2 . The contribution from all other background processes estimated from simulation in each bin in a given CR (N MC,bkg CR bin i ) is subtracted from the data yield in the corresponding bin in the CR (N data CR bin i ), and compared to the MC prediction (N MC,tt CR bin i ) to derive the correction factor: Finally, the prediction for the tt background in the SR (N tt SR bin i ) is: where N MC,tt SR bin i is the prediction for the SR from the MC simulation. Because the tt-enriched sample is the purer of the two, the corrections are first derived in this sample. These corrections are applied to the tt simulation in the W( ν)+jets-enriched sample, and then analogous corrections and predictions for the W( ν)+jets background process are derived.
The corrections based on M R and R 2 are measured and applied by averaging over all jet multiplicity bins. As our SRs are divided according to the jet multiplicity, additional corrections are needed in order to ensure correct background modeling for different numbers of jets. We derive these corrections separately for the tt and W( ν)+jets samples, obtaining correction factors for events with two or three jets, four to six jets, and seven or more jets. The tt correction is derived prior to the W( ν)+jets correction to take advantage of the slightly higher purity of the tt CR.
We also check for MC mismodeling that depends on the number of b jets in the event. To do this we apply the above-mentioned corrections in bins of M R , R 2 , and the number of jets and derive an additional correction needed to make the predicted M R spectrum match that in data for each b tag multiplicity. This correction is performed separately for events with two or three, four to six, and seven or more jets.
A final validation of the MC modeling in this one-lepton CR is completed by comparing the R 2 spectrum in data with the MC prediction in each jet multiplicity and b tag multiplicity category. We do not observe any systematic mismodeling in the R 2 spectra, and we propagate the total uncertainty in the data-to-MC ratio in each bin of R 2 as a systematic uncertainty in the tt and W+jets backgrounds in the analysis SRs.
The tt background in the one-lepton CR is composed mostly of lepton+jets tt events, where one top quark decayed fully hadronically and the other top quark decayed leptonically. In the leptonic analysis SRs, the m T requirement suppresses lepton+jets tt events, and the dominant  remaining tt background consists of tt events where both top quarks decayed leptonically, and one of the two leptons is not identified. It is therefore important to validate that the corrections to the tt simulation derived in the one-lepton CR also describe dileptonic tt events well. We perform this check by selecting an event sample enriched in dileptonic tt events, applying the corrections on the tt simulation prediction derived in the one-lepton CR, and evaluating the consistency of the data with the corrected prediction. This check is performed separately for each jet multiplicity category used in the analysis SRs. The dilepton tt-enriched sample consists of events with two tight electrons or muons with p T > 30 GeV and invariant mass larger than 20 GeV, at least one b-tagged jet with p T > 40 GeV, and p miss T > 40 GeV. Events with two sameflavor leptons with invariant mass between 76 and 106 GeV are rejected to suppress Drell-Yan background. The p miss T and the m T variables are computed treating one of the leptons in each event as visible and the other as invisible, and the requirement on the m T is subsequently applied. A systematic uncertainty in the dilepton tt background is assessed by comparing data with the MC prediction in the M R distribution for each jet multiplicity category. The M R distributions in the tt dilepton CR for the two to three and four to six jet event categories are displayed in the upper row of Fig. 2.
The MC prediction for the hadronic SRs can be affected by potential mismodeling of the veto identification efficiency for electrons, muons, and τ h candidates. The veto lepton and veto τ h CRs are defined in order to assess the modeling of this efficiency in simulation. Events in the veto lepton (veto τ h candidate) CR are required to have at least one veto lepton (τ h candidate) and pass one of the hadronic razor triggers. These events must also have m T between 30 and 100 GeV, M R > 400 GeV, R 2 > 0.25, and at least two jets with p T > 80 GeV. The data and MC prediction are compared in bins of lepton p T and η for each jet multiplicity category. A systematic uncertainty of about 25% is assigned to cover the difference between data and prediction in the lepton p T spectrum. No further systematic mismodeling is observed in the lepton η distributions, and the size of the uncertainty in each η bin is propagated as an uncertainty in the analysis SR predictions. The lepton p T distributions obtained in the veto lepton CR for the categories with two to three and four to six jets are displayed in the lower row of Fig. 2.

The Z → νν background
The background prediction for the Z(νν)+jets process is made using the same methodology as for the tt and W( ν) background processes. We take advantage of the kinematic similarities between the Z → , W( ν)+jets, and γ+jets processes [83][84][85]. Corrections to the hadronic recoil and jet multiplicity spectra are obtained in a control sample enriched in γ+jets events, and the validity of these corrections is checked in a second control sample enriched in W( ν)+jets events. A third control sample, enriched in Z → events, is used to normalize the obtained correction factors and to provide an additional consistency check of the MC prediction.
The γ+jets control sample consists of events having at least one selected photon and passing a set of kinematic requirements. Photons are required to have p T > 185 GeV and pass loose identification and isolation criteria. The photon is treated as invisible-its p T is added vectorially to the p miss T , and it is ignored in the calculation of M R -in order to simulate the invisible Z boson decay products in a Z → νν+jets event. Selected events must pass a single-photon trigger, have two jets with p T > 80 GeV, and have M R > 400 GeV and R 2 > 0.25.
The contribution of misidentified photons to the yield in this control sample is estimated via a template fit to the distribution of the photon charged isolation, the p T sum of all charged PF particles within a ∆R cone of size 0.4 centered on the photon momentum axis. The fit is performed in bins of M R and R 2 and yields an estimate of the purity of the photon sample in each bin. Contributions from other background processes such as ttγ are estimated using simulation and account for about 1-2%. Additionally, events in which the photon is produced within a jet are considered to be background. Corrections to the hadronic recoil in simulation are derived in this CR by subtracting the estimated background yields from the number of observed counts, and comparing the resulting yield with the prediction from the γ+jets simulation, in each bin of M R and R 2 .
As in the one-lepton CR described in Section 5.1, an additional correction is derived to account for possible mismodeling in simulation as a function of the jet multiplicity. This correction is derived for events with two or three jets, with four to six jets, and with seven or more jets. After these corrections are applied, the data in the CR are compared with the MC prediction in bins of the number of b-tagged jets. As in the one-lepton CR, the M R spectra in simulation are corrected to match the data in each b tag category, and a systematic uncertainty in the Z(νν)+jets background is assigned based on the size of the uncertainty in each bin of R 2 .
A check of the Z(νν)+jets prediction is performed with a sample enriched in Z → decays. Events in this sample are required to have two tight electrons or two tight muons having an invariant mass consistent with the Z mass. The two leptons are treated as invisible for the purpose of computing the razor variables. Events must have no b-tagged jets, two or more jets with p T > 80 GeV, M R > 400 GeV, and R 2 > 0.25. The correction factors obtained from the γ+jets CR are normalized so that the total MC prediction in the Z → + − +jets CR matches the observed data yield. This corrects for the difference between the true γ+jets cross section and the leading order cross section used to normalize the simulated samples. The M R distributions in this CR for the two to three and four to six jet categories are shown in Fig. 3. The observed residual disagreements between data and simulation in the M R and R 2 distributions are propagated as systematic uncertainties in the Z(νν)+jets prediction.
The MC corrections derived in the γ+jets CR are checked against a second set of corrections derived in a CR enriched in W( ν)+jets events. This CR is identical to the W( ν)+jets sample described in Section 5.1, except that the selected lepton is treated as invisible for the purpose of computing M R and R 2 . Correction factors are derived in the same way as in the W( ν)+jets CR. The full difference between these corrections and those obtained from the γ+jets CR is taken as a systematic uncertainty in the Z(νν)+jets prediction in the SR, and is typically between 10 and 20%, depending on the bin.

The QCD multijet background
Multijet events compose a nonnegligible fraction of the total event yield in the hadronic SRs. Such events are characterized by a significant undermeasurement of the energy of a jet, and consequently a large amount of p miss T , usually pointing towards the mismeasured jet. A large fraction of QCD multijet events are rejected by the requirement that the azimuthal angle ∆φ R between the axes of the two razor megajets is less than 2.8. We treat the events with ∆φ R ≥ 2.8 as a CR of QCD multijet events, while the events with ∆φ R < 2.8 define the SRs.
We estimate the number of QCD multijet events in this CR in bins of M R and R 2 by subtracting the predicted contribution of other processes from the total event yield in each bin. This is done for each jet multiplicity category. We observe in simulation that the fraction of QCD multijet events at each b tag multiplicity is independent of M R , R 2 , and ∆φ R . The event yields in the QCD CRs are therefore measured inclusively in the number of b tags and then scaled according to the fraction of QCD multijet events at each multiplicity of b-tagged jets.
We then predict the number of QCD multijet events in the SRs via the transfer factor ζ, defined as The QCD background prediction in each bin (N QCD SR bin i ) is made as: where N data CR bin i is the number of events observed in the data CR and N bkg CR bin i is the contribution from background processes other than the QCD multijet process and is predicted from the corrected MC.
We observe in simulation that ζ changes slowly with M R and increases roughly linearly with R 2 . In data we therefore compute ζ in bins of M R and R 2 in a low-R 2 region defined by 0.20 < R 2 < 0.30 and fit the computed values with a linear function in M R and R 2 . We then use the linear fit and its uncertainty to estimate the value of ζ in the analysis SRs. The fit is performed separately in each category of jet multiplicity, but inclusively in the number of b-tagged jets, as ζ is observed in simulation not to depend on the b tag multiplicity. For the category with seven or more jets, the fit function is allowed to depend on R 2 only, because of the low number of events in the fit region.
The statistical uncertainty in the CR event counts and the fitted uncertainty of the transfer factor extrapolation are propagated as systematic uncertainties of the QCD multijet background prediction. Another systematic uncertainty of 30% is propagated in order to cover the dependence of the transfer factor on the number of b-tagged jets in different CRs. Furthermore, we make an alternative extrapolation for the transfer factor where we allow a dependence on M R and R 2 for the Seven-jet category, and a quadratic dependence on M R for the Dijet and Multijet categories. The difference in the QCD multijet background prediction between the default and alternative transfer factor extrapolation is propagated as an additional systematic uncertainty, whose size ranges from 10% for M R below 1 TeV to 70-90% for M R above 1.6 TeV.

Background modeling in boosted event categories
The dominant SM background processes in the boosted categories are the same as in the nonboosted categories. An additional, but important source of background comes from processes where one of the jets in the event is mistagged as a boosted hadronic W boson or top quark.
Requiring boosted objects in the selection results in a smaller number of events in the SRs or CRs. As a general rule, in cases where no MC events exist in SR bins for a given background process, MC counts in these bins are extrapolated from a looser version of the signal selection obtained by relaxing the N-subjettiness criteria for Wor t tagging. For cases where there are no counts or very low statistical precision in the CR bins, these depleted bins are temporarily merged to obtain coarser bins with increased event count. Background estimation is done in two steps, where first the yields are estimated using the coarser bins, and next, the yields in coarse bins are distributed to the finer bins proportional to the background MC counts in the finer bins.

The tt+jets and W+jets background estimation for the boosted categories
The CRs for the tt and W+jets backgrounds are defined similar to the CRs used for the nonboosted categories. We require exactly one veto electron or muon. To suppress contamination from signal processes, m T is required to be less than 100 GeV. To mimic the signal selection, the ∆φ R < 2.8 requirement is applied. To estimate the top quark background for the boosted W 4-5 jet and boosted W 6 jet SR categories, we require events in the CR to have at least one boosted W boson and one b-tagged jet, while for the boosted top category, we require one boosted top quark. To estimate the W( ν)+jets background for the boosted W 4-5 jet and boosted W 6 jet SR   Figure 4 shows the b-tagged jet multiplicity distribution, identified with the medium b jet tagger, for events in the boosted W 6 jet category in the tt CR before applying the b tagging selection, and the m T distribution in the boosted top category in the tt CR before applying the m T selection. Figure 5 shows the distribution in M R and R 2 bins for events in the boosted top category in the tt CR, and for events in the boosted W 4-5 jet and boosted W 6 jet categories in the W( ν)+jets CR. The purity of tt+jets and single top events in the tt CR is more than 80%, and the purity of the W( ν)+jets process in the W( ν)+jets CR is also larger than 80%.

The Z → νν+jets background estimation for the boosted categories
The background estimate for the Z → νν+jets process is again similar to the method used for the nonboosted categories. We make use of the similarity in the kinematics of the photon in γ+jets events and the Z boson in Z+jets events to select a control sample of γ+jets to mimic the behavior of Z → νν+jets events. The γ+jets CR is selected by requiring exactly one photon with p T > 80 GeV from data collected by jet and H T triggers.      veto is applied, and ∆φ R , computed after treating the photon as invisible, is required to be less than 2.8. One W-tagged or t-tagged jet is required for the boosted Wand top categories, respectively. Figure 6 shows the M R -R 2 distribution for the boosted top category. The QCD multijet contribution to the γ+jets CR is accounted for by a template fit to the photon charged isolation variable in inclusive bins of M R and R 2 . Other background processes in the γ+jets CRs are small and predicted using MC. Finally, the SR prediction for the Z → νν+jets background is extrapolated from the γ+jets yields via the MC transfer factor λ Z→νν = N SR,MC Z→νν /N CR,MC γ+jets . We perform a cross check on the previous estimate using a CR enhanced in Z → events. The Z → CR is defined by requiring exactly two tight electrons or muons with p T > 10 GeV and dilepton mass satisfying |m − m Z | < 10 GeV, where m Z is the Z boson mass. All other requirements are the same as those for the γ+jets CR. The momentum of the dilepton system is added vectorially to p miss T to mimic an invisible decay of the Z boson. Similar to the procedure for the nonboosted categories, the comparison between data and MC yields in the Z → CR are used to correct the MC transfer factor λ to account for the impact of missing higher order corrections on the total normalization predicted by the γ+jets simulation.
As for the inclusive categories, we obtain an alternative estimate from the W(→ ν)+jetsenriched CR to validate the predictions from the γ+jets CR. We require the presence of exactly one tight electron or muon. m T is required to be between 30 and 100 GeV. The rest of the selection is the same as for the γ+jets CR. The lepton momentum is added vectorially to p miss T to mimic an invisible decay. The W(→ ν)+jets CR yields are extrapolated to the SR via transfer factors calculated from simulation to obtain the alternative Z → νν+jets background estimate. Figure 7 compares the estimates from the γ+jets CR, the W(→ ν)+jets CR, and the MC simulation. The difference between the two alternative estimates based on CRs in data is propagated as a systematic uncertainty.

Multijet background estimation in the boosted categories
The CR enriched in QCD multijet background is defined by inverting the ∆φ R requirement, and requiring antitagged W boson or top quark candidates by inverting the N-subjettiness criteria and subjet b tagging for t-tagged jets. Figure 8 shows the distribution in the M R and R 2 bins for the boosted W 4-5 jet, boosted W 6 jet and boosted top categories. The purity achieved with the selection described above is about 90%. The QCD multijet background is predicted by extrapolating the event yields from this QCD multijet CR to the SRs via transfer factors calculated from simulation.
The effects of inaccuracies in the QCD multijet MC modeling on the multijet background estimate are taken into account by propagating a systematic uncertainty computed based on the level of disagreement between data and simulation in the b jet multiplicity, N-subjettiness and ∆φ R distributions before applying these selections. The resulting overall systematic uncertainties are 13 and 24% for boosted Wand top categories, respectively.

Validating the background estimation with closure tests in boosted categories
Two validations are performed in CRs similarly to that for the QCD multijet CR but by inverting only one of the two requirements. These validations are intended to verify the reliability of the background estimates in the boosted categories.
The first validation is performed in a CR that is defined identically to the SR except that we invert the ∆φ R requirement. The comparison between data and predicted background validates the MC modeling of b tagging, the ∆φ R shape, the extrapolation in the lepton multiplicity, and the accuracy of the efficiency for W boson and top quark tagging. Figure 9 shows the results for the boosted W 4-5 jet, boosted W 6 jet, and boosted top categories. Overall, the estimation agrees with data within uncertainties.
The second validation is performed in a CR defined identically to the SR but requiring antitagged W boson or top quark candidates. This validation is designed to check the modeling of the ∆φ R variable in the QCD multijet and Z(νν)+jets simulation. The plots in Fig. 10 show the estimation results compared to data for the boosted W 4-5 jet, boosted W 6 jet, and boosted top categories. Overall, the estimation agrees with data within uncertainties.

Systematic uncertainties
Systematic uncertainties considered in this analysis can be broadly categorized into three types: uncertainties from the limited accuracy of calibrations, auxiliary measurements, and theoretical predictions; uncertainties from the data-driven background prediction methodology; and uncertainties specific to the fast simulation prediction of the signal.
Systematic uncertainties of the first type are propagated as shape uncertainties in the signal and background predictions in all event categories. Uncertainties in the trigger and lepton selection efficiency, and in the integrated luminosity [86], primarily affect the total normalization. Uncertainties in the b tagging efficiency affect the relative yields between different b tag categories. Systematic uncertainties in the modeling of the W boson and top quark tagging and mistagging efficiencies affect the yields of the boosted categories. The uncertainties from missing higherorder corrections and the uncertainties in the jet energy and lepton momentum scales affect the shapes of the M R and R 2 distributions. In Table 3 we summarize these systematic uncertainties and their typical impact on the background and signal predictions.
The second type of systematic uncertainty is related to the background prediction methodol-       ogy. Statistical uncertainties of the CR data range from 1-20% depending on the M R and R 2 bin. Systematic uncertainties of the background processes that we are not targeting in each CR contribute at the level of a few percent. Systematic uncertainties related to the accuracy of assumptions made by the background estimation method are estimated through closure tests in different CRs as discussed in Section 5. These systematic uncertainties capture the potential modeling inadequacies of the simulation after applying the corrections derived as part of the analysis procedure. They are summarized in Table 4.
For the closure tests performed in each N jets bin in the tt dilepton and the Z(νν)+jets dilepton CRs, and the test of the p T distributions in the veto lepton and veto τ h CRs, the uncertainties are applied correlated across all bins. For the checks of the R 2 distributions in each b tag category in the one-lepton and photon CRs, and of the lepton η distributions in the veto lepton and veto τ h CRs, the systematic uncertainties are assigned based on the size of the statistical uncertainty in the CRs and are assumed to be uncorrelated from bin to bin.
For the Z(νν)+jets process, the difference in the correction factors computed in the γ+jets and one-lepton CRs are propagated as a systematic uncertainty. This systematic uncertainty estimates the potential differences in the MC mismodeling of the hadronic recoil between the γ+jets process and the Z(νν)+jets process. These systematic uncertainties range up to 20%.
Finally, there are systematic uncertainties specific to the fast simulation prediction of the signal. These include systematic uncertainties because of possible inaccuracies of the fast simulation in modeling the efficiencies for lepton selection, b tagging, and boosted W boson and top quark tagging. To account for possible mismodeling of the signal acceptance because of differences in the data and signal MC pileup distributions, we employ a linear fit that extrapolates the acceptance in each analysis bin to the range of pileup values observed in data. Uncertainty in this method is propagated to the signal yield predictions. An additional uncertainty is applied to account for known tendencies for the fast simulation to mismodel the p miss T in some events. Finally, we propagate an uncertainty in the modeling of the ISR for signal predictions, ranging from 4-25% depending on the number of jets from ISR.

Results and interpretation
The observed data yields in the SRs are statistically compatible with the background prediction from SM processes. The results are summarized in the distributions of the M R and R 2 bins of the SRs. The results for the one-lepton categories are shown in Figs. 11-14. The main backgrounds are W+jets and tt production, with tt becoming more dominant with increasing number of b-tagged jets. The three example signals used to interpret the results are also shown.
The results for the zero-lepton boosted categories are shown in Fig. 15, where tt is the dominant background process in all subcategories.
Finally, the results for the zero-lepton nonboosted categories are shown in Figs. [16][17][18][19][20][21]. The Z(νν)+jets background is dominant for subcategories with fewer jets and b-tagged jets, while the tt background is dominant for subcategories with more jets and b-tagged jets.
We set upper limits on the production cross sections of various SUSY simplified models. We follow the LHC CL s procedure [87][88][89] by using the profile likelihood ratio test statistic and the asymptotic formula to evaluate the 95% confidence level (CL) observed and expected limits on the production cross section. Systematic uncertainties are propagated by incorporating nuisance parameters that represent different sources of systematic uncertainty, which are profiled in the maximum likelihood fit [89].
Generally, the best signal sensitivity comes from the Lepton Multijet and Multijet categories, and are dominated by bins with large M R when the mass splitting between the gluino (or squark) and the LSP is large, and by bins with large R 2 when the mass splitting is small. For signal models that produce many jets, such as gluino pair production with gluinos decaying to two top quarks and the LSP, the Lepton Seven-jet and Seven-jet categories dominate the sensitivity. For signal models with boosted top quarks, such as top squark pair production, the boosted categories contribute significantly to the sensitivity.
First, we consider the scenario of pair produced gluinos decaying to two top quarks and the LSP. The expected and observed limits for such gluinos decays are shown as a function of gluino and LSP masses in Fig. 22. In this simplified model, we exclude gluino masses up to 2.0 TeV for LSP mass below 700 GeV. The limit for gluinos decaying to a top quark and a low                  Figure 17: The M R -R 2 distribution observed in data is shown along with the background prediction obtained for the Dijet event category in the 2 or more b tag bin. Further details of the plots are explained in the caption of Fig. 11. mass top squark that subsequently decays to a charm quark and the LSP, is shown in Fig. 23. For this simplified model, we exclude gluino masses up to 1.9 TeV for LSP mass above 150 and below 950 GeV, extending the previous best limits [35] from the CMS experiment by about 100 GeV in the gluino mass. Finally, we consider pair produced top squarks decaying to the top quark and the LSP. The expected and observed limits are shown in Fig. 24, and we exclude top squark masses up to 1.14 TeV for LSP mass below 200 GeV, extending the previous best limits [29] from the CMS experiment by about 20 GeV. The dashed blue contour in each exclusion limit plot represents the expected limit obtained using data from the nonboosted categories only. By comparing the expected limits obtained using only the nonboosted categories with the expected limits using all categories, we observe clearly that the boosted categories make an important contribution to the sensitivity for the signal models presented here.

Summary
We have presented an inclusive search for supersymmetry (SUSY) in events with no more than one lepton, a large multiplicity of energetic jets, and evidence of invisible particles using the razor kinematic variables. To enhance sensitivity to a broad range of signal models, the events are categorized according to the number of leptons, the presence of jets consistent with hadronically decaying W bosons or top quarks, and the number of jets and b-tagged jets. The analysis uses √ s = 13 TeV proton-proton collision data collected by the CMS experiment in 2016 and corresponding to an integrated luminosity of 35.9 fb −1 . Standard model backgrounds were estimated using control regions in data and Monte Carlo simulation yields in signal and control regions. Background estimation procedures were verified using validation regions with kinematics resembling that of the signal regions and closure tests. Data are observed to be consistent with the standard model expectation.  Multijet 0 b tag Data / pred.

Multijet 3 b tag
Data / pred.  Figure 19: The M R -R 2 distribution observed in data is shown along with the background prediction obtained for the Multijet event category in the 2 b tag (upper) and 3 or more b tag (lower) bins. Further details of the plots are explained in the caption of Fig. 11.
95% CL upper limit on cross section (pb) Figure 22: Expected and observed 95% CL limits on the production cross section for pairproduced gluinos each decaying to the LSP and top quarks. The blue dashed contour represents the expected 95% CL upper limit using data in the nonboosted categories only.
The results were interpreted in the context of simplified models of pair-produced gluinos and direct top squark pair production. Limits on the gluino mass extend to 2.0 TeV, while limits on top squark masses reach 1.14 TeV. The combination of a large variety of final states enables this analysis to improve the sensitivity in various signal scenarios. The analysis extended the exclusion limit of the gluino mass from the CMS experiment by ≈100 GeV in decays to a lowmass top squark and a top quark, and the exclusion limit of the top squark mass by ≈20 GeV in direct top squark pair production. 95% CL upper limit on cross section (pb) Figure 23: Expected and observed 95% CL limits on the production cross section for pairproduced gluinos each decaying to a top quark and a low mass top squark that subsequently decays to a charm quark and the LSP. The mass splitting (m t − m χ 0 1 ) is fixed to be 20 GeV. The blue dashed contour represents the expected 95% CL upper limit using data in the nonboosted categories only. 95% CL upper limit on cross section (pb) Figure 24: Expected and observed 95% CL limits on the production cross section for pairproduced squarks each decaying to a top quark and the LSP. The blue dashed contour represents the expected 95% CL upper limit using data in the nonboosted categories only. The white diagonal band corresponds to the region |m t − m t − m χ 0 1 | < 25 GeV, where the mass difference between the t and the χ 0 1 is very close to the top quark mass. In this region the signal acceptance depends strongly on the χ 0 1 mass and is therefore difficult to model.  [36] CMS Collaboration, "Searches for pair production of third-generation squarks in √ s = 13 TeV pp collisions", Eur. Phys. J. C 77 (2017) 327, doi:10.1140/epjc/s10052-017-4853-2, arXiv:1612.03877. [39] ATLAS Collaboration, "Search for squarks and gluinos in events with an isolated lepton, jets, and missing transverse momentum at √ s = 13 TeV with the ATLAS detector", Phys. Rev. D 96 (2017) 112010, doi:10.1103/PhysRevD.96.112010, arXiv:1708.08232.