Search for squarks and gluinos in final states with jets and missing transverse momentum using 36 fb − 1 of p = 13 TeV pp collision data with the ATLAS detector

A search for the supersymmetric partners of quarks and gluons (squarks and gluinos) in final states containing hadronic jets and missing transverse momentum, but no electrons or muons, is presented. The data used in this search were recorded in 2015 and 2016 by the ATLAS experiment in ﬃﬃﬃ s p ¼ TeV proton-proton collisions at the Large Hadron Collider, corresponding to an integrated luminosity of 36 . 1 fb − 1 . The results are interpreted in the context of various models where squarks and gluinos are pair produced and the neutralino is the lightest supersymmetric particle. An exclusion limit at the 95% confidence level on the mass of the gluino is set at 2.03 TeV for a simplified model incorporating only a gluino and the lightest neutralino, assuming the lightest neutralino is massless. For a simplified model involving the strong production of mass-degenerate first- and second-generation squarks, squark masses below 1.55 TeVare excluded if the lightest neutralino is massless. These limits substantially extend the region of supersymmetric parameter space previously excluded by searches with the ATLAS detector. and the dotted lines are obtained by varying the signal cross section by the renormalization and factorization scale and PDF uncertainties. Results are compared with the observed limits obtained by the previous ATLAS searches with jets, missing transverse momentum, and no leptons [11].


I. INTRODUCTION
Supersymmetry (SUSY) [1][2][3][4][5][6] is a generalization of space-time symmetries that predicts new bosonic partners for the fermions and new fermionic partners for the bosons of the Standard Model (SM). If R-parity is conserved [7], SUSY particles, called sparticles, are produced in pairs and the lightest supersymmetric particle (LSP) is stable and represents a possible dark-matter candidate. The scalar partners of the left-and right-handed quarks, the squarks q L andq R , mix to form two mass eigenstatesq 1 andq 2 ordered by increasing mass. Superpartners of the charged and neutral electroweak and Higgs bosons also mix, producing charginos (χ AE ) and neutralinos (χ 0 ). Squarks and the fermionic partners of the gluons, the gluinos (g), could be produced in strong-interaction processes at the Large Hadron Collider (LHC) [8] and decay via cascades ending with the stable LSP, which escapes the detector unseen, producing substantial missing transverse momentum ( ⃗ E miss T ). The large cross sections predicted for the strong production of supersymmetric particles make the production of gluinos and squarks a primary target in searches for SUSY in proton-proton (pp) collisions at a center-of-mass energy of 13 TeV at the LHC. Interest in these searches is motivated by the large available choice of parameters for R-parity-conserving models in the minimal supersymmetric Standard Model (MSSM) [9,10] where squarks (including antisquarks) and gluinos can be produced in pairs (gg, qq,qg) and can decay throughq → qχ 0 1 andg → qqχ 0 1 to the lightest neutralino,χ 0 1 , assumed to be the LSP. Additional decay modes can include the production of charginos viaq → qχ AE (whereq and q are of different flavor) andg → qqχ AE , or neutralinos viag → qqχ 0 2 . Subsequent chargino decay to W AEχ0 1 or neutralino decay to Zχ 0 1 or hχ 0 1 , depending on the decay modes of W, Z, and h bosons, can increase the jet multiplicity and missing transverse momentum.
This paper presents two approaches to search for these sparticles in final states containing only hadronic jets and large missing transverse momentum. The first is an update of the analysis [11] (referred to as "Meff-based search" in the following). The second is a complementary search using the recursive jigsaw reconstruction (RJR) technique [12][13][14] in the construction of a discriminating variable set ("RJR-based search"). By using a dedicated set of selection criteria, the RJR-based search improves the sensitivity to supersymmetric models with small mass splittings between the sparticles (models with compressed spectra). Both searches presented here adopt the same general approach as the analysis of the 7, 8, and 13 TeV data collected during Run 1 and Run 2 of the LHC, described in Ref. [11].
In the searches presented here, events with reconstructed electrons or muons are rejected to avoid any overlap with a complementary ATLAS search in final states with one lepton, jets, and missing transverse momentum [19], and to reduce the background from events with neutrinos (W → eν; μν). The selection criteria are optimized in the m˜g; m˜χ0 1 and mq; m˜χ0 1 planes, (where mg, mq, and m˜χ0 1 are the gluino, squark, and LSP masses, respectively) for simplified models [20][21][22], and in the mg; mq plane for the simplified phenomenological MSSM (pMSSM) models [23,24] in which the number of MSSM parameters is reduced using existing experimental and theoretical constraints. Although interpreted in terms of SUSY models, the results of this analysis could also constrain any model of new physics that predicts the production of jets in association with missing transverse momentum.
The paper is organized as follows. Section II describes the ATLAS experiment and data samples used, and Sec. III Monte Carlo (MC) simulation samples used for background and signal modeling. Event reconstruction and identification are presented in Sec. IV. The analysis strategy used by both searches is given in Sec. V. Since the RJR technique is a new approach for this search, Sec. VI is dedicated to the description of the technique and associated variables. Searches are performed in signal regions that are defined in Sec. VII. Summaries of the background estimation methodology and corresponding systematic uncertainties are presented in Secs. VIII and IX, respectively. Results obtained using the signal regions optimized for both searches are reported in Sec. X. Section XI is devoted to conclusions.

II. THE ATLAS DETECTOR AND DATA SAMPLES
The ATLAS detector [25] is a multipurpose detector with a forward-backward symmetric cylindrical geometry and nearly 4π coverage in solid angle. 1 The inner detector (ID) tracking system consists of pixel and silicon microstrip detectors covering the pseudorapidity region jηj < 2.5, surrounded by a transition radiation tracker, which improves electron identification over the region jηj < 2.0. The innermost pixel layer, the insertable B-layer [26], was added between Run 1 and Run 2 of the LHC, at a radius of 33 mm around a new, narrower, and thinner beam pipe. The ID is surrounded by a thin superconducting solenoid providing an axial 2 T magnetic field and by a fine-granularity lead/liquid-argon (LAr) electromagnetic calorimeter covering jηj < 3.2. A steel/scintillator-tile calorimeter provides hadronic coverage in the central pseudorapidity range (jηj < 1.7). The endcap and forward regions (1.5 < jηj < 4.9) are made of LAr active layers with either copper or tungsten as the absorber material for electromagnetic and hadronic measurements. The muon spectrometer with an air-core toroid magnet system surrounds the calorimeters. Three layers of high-precision tracking chambers provide coverage in the range jηj < 2.7, while dedicated chambers allow triggering in the region jηj < 2.4.
The ATLAS trigger system [27] consists of two levels; the first level is a hardware-based system, while the second is a software-based system called the high-level trigger. The events used by the searches described in this paper were selected using a trigger logic that accepts events with a missing transverse momentum above 70 GeV (for data collected during 2015) or above  GeV (depending on data-taking period for data collected in 2016) calculated using a vectorial sum of the jet transverse momenta. The trigger is 100% efficient for the event selections considered in these analyses. Auxiliary data samples used to estimate the yields of background events were selected using triggers requiring at least one isolated electron (p T > 24 GeV), muon (p T > 20 GeV), or photon (p T > 120 GeV) for data collected in 2015. For the 2016 data, the events used for the background estimation were selected using triggers requiring at least one isolated electron or muon (p T > 26 GeV) or photon (p T > 140 GeV).
The data were collected by the ATLAS detector during 2015 with a peak delivered instantaneous luminosity of L ¼ 5.2 × 10 33 cm −2 s −1 , and during 2016 with a maximum of L ¼ 1.37 × 10 34 cm −2 s −1 . The mean number of pp interactions per bunch crossing in the data set was 14 in 2015 and 24 in 2016. Application of beam, detector, and data-quality criteria resulted in a total integrated luminosity of 36.1 fb −1 . The uncertainty in the integrated luminosity averaged over both years is 3.2%. It is derived, following a methodology similar to that detailed in Ref. [28], from a preliminary calibration of the luminosity scale using a pair of x-y beam-separation scans performed in August 2015 and May 2016.

III. MONTE CARLO SAMPLES
A set of simulated MC event samples was used to optimize the selections, estimate backgrounds, and assess the sensitivity to specific SUSY signal models.
Simplified models and pMSSM models are both used as SUSY signals in this paper. Simplified models are defined 1 ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point in the center of the detector. The positive x axis is defined by the direction from the interaction point to the center of the LHC ring, with the positive y axis pointing upwards, while the beam direction defines the z axis. Cylindrical coordinates ðr; ϕÞ are used in the transverse plane, ϕ being the azimuthal angle around the z axis. The pseudorapidity η is defined in terms of the polar angle θ by η ¼ − ln tanðθ=2Þ and the rapidity is defined as y ¼ ð1=2Þ ln½ðE þ p z Þ=ðE − p z Þ where E is the energy and p z the longitudinal momentum of the object of interest. The transverse momentum p T , the transverse energy E T , and the missing transverse momentum E miss T are defined in the x-y plane unless stated otherwise. by an effective Lagrangian describing the interactions of a small number of new particles, assuming one production process and one decay channel with a 100% branching fraction. Signal samples are used to describe squark and gluino pair production, followed by the direct (q → qχ 0 1 ) or one-step (q → qWχ 0 1 ) decays of squarks and direct (g → qqχ 0 1 ) or one-step (g → qqW=Z=hχ 0 1 ) decays of gluinos as shown in Fig. 1. Direct decays are those where the considered SUSY particles decay directly into SM particles and the LSP, while the one-step decays refer to the cases where the decays occur via one intermediate on-shell SUSY particle, as indicated in parentheses. In pMSSM models, gluino and first-and second-generation squark production are considered inclusively, followed by direct decays of squarks and gluinos, or decays of squarks via gluinos (q → qg) and decays of gluinos via squarks (g → qq) if kinematically possible. All other supersymmetric particles, including the squarks of the third generation, have their masses set such that the particles are effectively decoupled. These samples were generated with up to two (simplified models) or one (pMSSM models) extra partons in the matrix element using the MG5_aMC@NLO 2.2.2 or 2.3.3 event generator [29] interfaced to PYTHIA 8.186 [30]. The CKKW-L merging scheme [31] was applied with a scale parameter that was set to a quarter of the mass of the gluino forgg production or of the squark forqq production in simplified models. In pMSSM models, a quarter of the smaller of the gluino and squark masses was used for the CKKW-L merging scale. The A14 [32] set of tuned parameters (tune) was used for initial/final-state radiation (ISR/FSR) and underlying-event parameters together with the NNPDF2.3LO [33] parton distribution function (PDF) set. The signal cross sections were calculated at next-to-leading order (NLO) in the strong coupling constant, adding the resummation of soft gluon emission at next-to-leading-logarithmic accuracy (NLO þ NLL) [34][35][36][37][38]. The nominal squark and gluino cross sections were taken from an envelope of predictions using different PDF sets and factorization and renormalization scales, as described in Ref. [39], considering only first-and second-generation squarks (ũ,d,s,c). Eightfold degeneracy of first-and second-generation squarks is assumed for the simplified models with direct decays of squarks and pMSSM models while fourfold degeneracy is assumed for the simplified models with one-step decays of squarks. In the case of gluino pair (squark pair) production in simplified models, cross sections were evaluated assuming arbitrarily high masses of 450 TeV for the first-and second-generation squarks (gluinos) in order to decouple them. The free parameters are m˜χ0 1 and mq (mg) for squark pair (gluino pair) production in simplified models, while both mq and mg are varied in pMSSM models with m˜χ0 1 fixed. In the simulation of the production of W or Z=γ Ã bosons in association with jets [40] using the SHERPA 2.2.1 event generator [41], the matrix elements were calculated for up to two partons at NLO and up to two additional partons at leading order (LO) using the COMIX [42] and OPEN LOOPS [43] matrix-element generators, and merged with the SHERPA parton shower [44] using the ME+PS@NLO prescription [45]. Simulated events containing a photon in association with jets were generated requiring a photon transverse momentum above 35 GeV. For these events, matrix elements were calculated at LO with up to three or four partons depending on the p T of the photon, and 1. Decay topologies of (a)-(c) squark pair production and (d)-(g) gluino pair production in the simplified models with (a) direct or (b),(c) one-step decays of squarks and (d) direct or (e)-(g) one-step decays of gluinos.
merged with the SHERPA parton shower using the ME+PS@LO prescription [46]. The W=Z þ jets events were normalized using their NNLO cross sections [47] while for the γ þ jets process the LO cross section, taken directly from the SHERPA MC event generator, was multiplied by a correction factor as described in Sec. VIII. For the generation of tt and single-top processes in the Wt and s-channel [48], the POWHEG-BOX v2 [49] generator was used, while electroweak (EW) t-channel single-top events were modeled using POWHEG-BOX v1. This latter generator uses the four-flavor scheme for the NLO matrixelement calculations together with the fixed four-flavor PDF set CT10f4 [50]. For each of these processes, the decay of the top quark was simulated using MADSPIN [51] preserving all spin correlations, while for all processes the parton shower, fragmentation, and the underlying event were generated using PYTHIA 6.428 [52] with the CTEQ6L1 [53] PDF set and the corresponding PERUGIA 2012 tune (P2012) [54]. The top quark mass was set to 172.5 GeV. The h damp parameter, which controls the p T of the first additional emission beyond the Born configuration, was set to the mass of the top quark in the tt process. The main effect of this parameter is to regulate the high-p T emission against which the tt system recoils [48]. The tt events were normalized using cross sections calculated at NNLO þ NNLL [55,56] accuracy, while s-and t-channel single-top events were normalized using the NLO cross sections [57,58], and the Wt-channel single-top events were normalized using the NNLO þ NNLL cross sections [59,60]. Production of a top quark in association with a Z boson is generated with the MG5_aMC@NLO 2.2.1 generator at LO with CTEQ6L1 PDF set.
For the generation of tt þ EW processes (ttþW=Z=WW) [61], the MG5_aMC@NLO 2.2.3 generator at LO interfaced to the PYTHIA 8.186 parton-shower model was used, with up to two [tt þ W, tt þ Zð→ νν=qqÞ], one [tt þ Zð→ llÞ], or no (tt þ WW) extra partons included in the matrix element. The events were normalized using their respective NLO cross sections [62,63] and the top quark mass was set to 172.5 GeV.
Diboson processes (WW, WZ, ZZ) [64] were simulated using the SHERPA 2.1.1 generator. For processes with four charged leptons (4l), three charged leptons and a neutrino (3l þ 1ν), or two charged leptons and two neutrinos (2l þ 2ν), the matrix elements contain all diagrams with four electroweak couplings, and were calculated for up to one (4l, 2l þ 2ν) or no partons (3l þ 1ν) at NLO. For processes in which one of the bosons decays hadronically and the other leptonically, matrix elements were calculated for up to one (ZZ) or no (WW, WZ) additional partons at NLO. All diboson samples also simulated up to three additional partons at LO using the COMIX and OPENLOOPS matrix-element generators, and were merged with the SHERPA parton shower using the ME+PS@NLO prescription.
A summary of the SUSY signals and the SM background processes together with the MC event generators, cross section calculation orders in α s , PDFs, parton shower, and tunes used is given in Table I.
For all SM background samples the response of the detector to particles was modeled with a full ATLAS detector simulation [65] based on GEANT4 [66]. Signal samples were prepared using a fast simulation based on a parametrization of the performance of the ATLAS electromagnetic and hadronic calorimeters [67] and on GEANT4 elsewhere. The EVTGEN v1.2.0 program [68] was used to describe the properties of the b-and c-hadron decays in the signal samples, and the background samples except those produced with SHERPA [41].
All simulated events were overlaid with multiple pp collisions simulated with PYTHIA 8.186 using the A2 tune [32] and the MSTW2008LO parton distribution functions [69]. The MC samples were generated with a variable number of additional pp interactions (pileup) and were reweighted to match the distribution of the mean number of interactions observed in data.

IV. EVENT RECONSTRUCTION AND IDENTIFICATION
The reconstructed primary vertex of the event is required to be consistent with the luminous region and to have at least two associated tracks with p T > 400 MeV. When more than one such vertex is found, the vertex with the largest P p 2 T of the associated tracks is chosen. Jet candidates are reconstructed using the anti-k t jet clustering algorithm [70,71] with a jet radius parameter of 0.4 starting from clusters of calorimeter cells [72]. The jets are corrected for energy from pileup using the method described in Ref.
[73]: a contribution equal to the product of the jet area and the median energy density of the event is subtracted from the jet energy [74]. Further corrections, referred to as the jet energy scale corrections, are derived from MC simulation and data, and are used to calibrate the average energies of jets to the scale of their constituent particles [75]. Only corrected jet candidates with p T > 20 GeV and jηj < 2.8 are retained. An algorithm based on boosted decision trees, 'MV2c10' [76,77], is used to identify jets containing a b-hadron (b-jets), with an operating point corresponding to an efficiency of 77%, and rejection factors of 134 for light-quark jets and 6 for charm jets [77] for reconstructed jets with p T > 20 GeV and jηj < 2.5 in simulated tt events. Candidate b-jets are required to have p T > 50 GeV and jηj < 2.5. Events with jets originating from detector noise and noncollision background are rejected if the jets fail to satisfy the "LooseBad" quality criteria, or if at least one of the two leading jets with p T > 100 GeV fails to satisfy the "TightBad" quality criteria, both described in Ref. [78]. The application of these requirements reduces the data sample by less than 1%. In order to reduce the number of jets coming from pileup, a significant fraction of the tracks associated with each jet must have an origin compatible with the primary vertex. This is enforced by using the jet vertex tagger (JVT) output using the momentum fraction of tracks [79]. The requirement JVT > 0.59 is only applied to jets with p T < 60 GeV and jηj < 2.4.
Two different classes of reconstructed lepton candidates (electrons or muons) are used in the analyses presented here. When selecting samples for the search, events containing a "baseline" electron or muon are rejected. The selections applied to identify baseline leptons are designed to maximize the efficiency with which W þ jets and top quark background events are rejected. When selecting "control region" samples for the purpose of estimating residual W þ jets and top quark backgrounds, additional requirements are applied to leptons to ensure greater purity of these backgrounds. These leptons are referred to as "high-purity" leptons below and form a subset of the baseline leptons.
Baseline muon candidates are formed by combining information from the muon spectrometer and inner detector as described in Ref. [80] and are required to have p T > 7 GeV and jηj < 2.7. High-purity muon candidates must additionally have p T > 27 GeV and jηj < 2.4, the significance of the transverse impact parameter with respect to the primary vertex jd PV 0 j=σðd PV 0 Þ < 3, and the longitudinal impact parameter with respect to the primary vertex jz PV 0 sinðθÞj < 0.5 mm. Furthermore, high-purity candidates must satisfy the "GradientLoose" isolation requirements described in Ref. [80], which rely on tracking-based and calorimeter-based variables and implement a set of ηand p T -dependent criteria.
Baseline electron candidates are reconstructed from an isolated electromagnetic calorimeter energy deposit matched to an ID track and are required to have p T > 7 GeV, jηj < 2.47, and to satisfy "Loose" likelihood-based identification criteria described in Ref. [81]. High-purity electron candidates additionally must satisfy "Tight" selection criteria described in Ref. [81], and the leading electron must have p T > 27 GeV. They are also required to have jd PV 0 j=σðd PV 0 Þ < 5, jz PV 0 sinðθÞj < 0.5 mm, and to satisfy isolation requirements similar to those applied to high-purity muons [81].
After the selections described above, ambiguities between candidate jets with jηj < 2.8 and leptons are resolved as follows: first, any such jet candidate that is not tagged as b-jet, lying within a distance ΔR ≡ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi ðΔηÞ 2 þ ðΔϕÞ 2 p ¼ 0.2 of a baseline electron is discarded. If a jet candidate is b-tagged it is interpreted as a jet and the overlapping electron is ignored. Additionally, if a baseline electron (muon) and a jet passing the JVT selection described above are found within 0.2 ≤ ΔR < 0.4 [< minð0.4; 0.04 þ 10 GeV=p μ T Þ], it is interpreted as a jet and the nearby electron (muon) candidate is discarded. Finally, if a baseline muon and jet are found within ΔR < 0.2, it is treated as a muon and the overlapping jet is ignored, unless the jet satisfies N trk < 3, where N trk refers to the number of tracks with p T > 500 MeV that are associated with the jet, in which case the muon is ignored. This criterion rejects jets consistent with final-state radiation or hard bremsstrahlung.
Additional ambiguities between electrons and muons in a jet, originating from the decays of hadrons, are resolved to avoid double counting and/or remove nonisolated leptons: the electron is discarded if a baseline electron and a baseline muon share the same ID track.
Reconstructed photons are used in the missing transverse momentum reconstruction as well as in the control region used to constrain the Z þ jets background, as explained in Sec. VIII. These latter photon candidates are required to satisfy p T > 150 GeV and jηj < 2.37, photon shower shape, and electron rejection criteria, and to be isolated [82]. The reduced η range for photons is chosen to avoid a region of coarse granularity at high η where photon and π 0 separation worsens. Ambiguities between candidate jets and photons (when used in the event selection) are resolved by discarding any jet candidates lying within ΔR ¼ 0.4 of a photon candidate. Additional selections to remove ambiguities between electrons or muons and photons are applied such that a photon is discarded if it is within ΔR ¼ 0.4 of a baseline electron or muon.
The measurement of the missing transverse momentum vector ⃗ E miss T (and its magnitude E miss T ) is based on the calibrated transverse momenta of all electron, muon, jet candidates, photons and all tracks originating from the primary vertex and not associated with such objects [83].
Initial jet-finding is extended using an approach called jet reclustering [84]. This allows the use of larger-radius-jet algorithms while maintaining the calibrations and systematic uncertainties associated with the input jets. Jets with a radius parameter 0.4 described above surviving the resolution of ambiguities and having p T > 25 GeV are used as input to an anti-k t algorithm with a jet radius parameter 1.0. A grooming scheme called "reclustered jet trimming" is applied to remove any small-radius jet constituent j of a large-radius reclustered jet J if p j T < f cut × p J T where the parameter f cut is set to be 0.05.
Corrections derived from data control samples are applied to account for differences between data and simulation for the lepton and photon trigger and reconstruction efficiencies, the lepton momentum/energy scale and resolution, and for the efficiency and mistag rate of the b-tagging algorithm.

V. ANALYSIS STRATEGY AND BACKGROUND PREDICTION
This section summarizes the common analysis strategy and statistical techniques that are employed in the searches presented in this paper.
To search for a possible signal, selection criteria are defined to enhance the expected signal yield relative to the SM backgrounds. Signal regions (SRs) are defined using the MC simulation of SUSY signals and the SM background processes. They are optimized to maximize the expected discovery sensitivity for each model considered.
To estimate the SM backgrounds in an accurate and robust fashion, control regions (CRs) are defined for each of the signal regions. They are chosen to be orthogonal to the SR selections in order to provide independent data samples enriched in particular backgrounds, and are used to normalize the background MC simulation. The CR selections are optimized to have negligible SUSY signal contamination for the models near the previously excluded boundary [11], while minimizing the systematic uncertainties arising from the extrapolation of the CR event yields to estimate backgrounds in the SR. Cross-checks of the background estimates are performed with data in several validation regions (VRs) selected with requirements such that these regions do not overlap with the CR and SR selections, and also have a low expected signal contamination.
In order to ensure sensitivity to the variety of squark and gluino production signals targeted in this search, a collection of inclusive SRs is considered. Each of the SR selection requirements is optimized to exploit expected differences in masses, kinematics, and jet multiplicities, and each represents its own counting experiment. Two different approaches are used in defining these SRs, with Meff-based and RJR-based selection criteria described in Secs. VII A and VII B, respectively. These two approaches are complementary because of differences in selected event populations and the strategy for balancing the signal-tobackground ratio against systematic uncertainties. A discussion of differences in these approaches is provided in Sec. VII C.
To extract the final results, three different classes of likelihood fits are employed: background-only, modelindependent, and model-dependent fits [85]. A background-only fit is used to estimate the background yields in each SR. The fit is performed using the observed event yields in the CRs associated with the SR as the only constraints, but not the yields in the SR itself. It is assumed that signal events from physics beyond the Standard Model (BSM) do not contribute to these CR yields. The scale factors represent the normalization of background components relative to MC predictions (μðW þ jetsÞ, μðZ þ jetsÞ, μðTopÞ), and are simultaneously determined in the fit to all the CRs associated with a SR. The expected background in the SR is based on the yields predicted by simulation for W=Z þ jets and background processes containing top quarks, corrected by the scale factors derived from the fit. In the case of multijet background, the estimate is based on the data-driven method described in Sec. VIII. The systematic and MC statistical uncertainties in the expected values are included in the fit as nuisance parameters that are constrained by Gaussian distributions with widths corresponding to the sizes of the uncertainties considered and by Poisson distributions, respectively. The background-only fit is also used to estimate the background event yields in the VRs.
A model-independent fit is used to quantify the level of agreement between background predictions and observed yields and to set upper limits on the number of BSM signal events in each SR. This fit proceeds in the same way as the background-only fit, where yields in the CRs are used to constrain the predictions of backgrounds in each SR, while the SR yield is also used in the likelihood with an additional nuisance parameter describing potential signal contributions. The observed and expected upper limits at 95% confidence level (C.L.) on the number of events from BSM phenomena for each signal region (S 95 obs and S 95 exp ) are derived using the CL s prescription [86], neglecting any possible signal contamination in the CRs. These limits, when normalized by the integrated luminosity of the data sample, may be interpreted as upper limits on the visible cross section of BSM physics (hϵσi 95 obs ), where the visible cross section is defined as the product of production cross section, acceptance, and efficiency. The model-independent fit is also used to compute the one-sided p-value (p 0 ) of the background-only hypothesis, which quantifies the statistical significance of an excess. Finally, a model-dependent fit is used to set exclusion limits on the signal cross sections for specific SUSY models. Such a fit proceeds in the same way as the model-independent fit, except that both the signal yield in the signal region and the signal contamination in the CRs are taken into account. Correlations between signal and background systematic uncertainties are taken into account where appropriate. Signal-yield systematic uncertainties due to detector effects and the theoretical uncertainties in the signal acceptance are included in the fit.

VI. THE RECURSIVE JIGSAW RECONSTRUCTION TECHNIQUE
The RJR technique [12][13][14] is a method for defining kinematic variables event by event. While it is straightforward to fully describe an event's underlying kinematic features when all objects are fully reconstructed, events involving invisible weakly interacting particles present a challenge, as the loss of information from escaping particles constrains the kinematic variable construction to take place in the lab frame instead of the more physically natural frames of the hypothesized decays. The RJR method partially mitigates this loss of information by determining approximations of the rest frames of intermediate particle states in each event. This reconstructed view of the event gives rise to a natural basis of kinematic observables, calculated by evaluating the momenta and energy of different objects in these reference frames.
All jets with p T > 50 GeV and jηj < 2.8 and the missing transverse momentum are used as input to the RJR algorithm. Motivated by searches for strong production of sparticles in R-parity-conserving models, a decay tree, shown in Fig. 2(a), is used in the analysis of events. Each event is evaluated as if two sparticles (the intermediate states P a and P b ) were produced and then decayed to the particles observed in the detector (the collections V a and V b ). The benchmark signal models probed in this search give rise to signal events with at least two weakly interacting particles associated with two systems of invisible particles (I a and I b ), the respective children of the initially produced sparticles.
This decay tree includes several kinematic and combinatoric unknowns. In the final state with no leptons, the objects observed in the detector are exclusively jets and it is necessary to decide how to partition these jets into the two groups V a and V b in order to calculate the observables associated with the decay tree. In this analysis, the grouping that minimizes the masses of the four-momentum sum of group constituents is chosen.
More explicitly, the collection of reconstructed jet fourmomenta, V ≡ fp i g and their four-momentum sum p V are considered. Each of the four-momenta is evaluated in the rest frame of p V (V frame) and different partitions of these jets For each partition, the sum of four-momenta p V i ¼ P N i j¼1 p j is calculated and the combination that maximizes the sum of momentum of the two groups, j ⃗p V a j þ j⃗p V b j, is chosen. The axis that this partition implicitly defines in the V rest frame is equivalent to the thrust axis of the jets, and the masses M V i ¼ (a) Inclusive strong sparticle production decay tree. Two sparticles (P a and P b ) are nonresonantly pair produced with each decaying to one or more visible particles (V a and V b ) that are reconstructed in the detector, and two systems of invisible particles (I a and I b ) whose four-momenta are only partially constrained. (b) An additional level of decays can be added when requiring more than two visible objects. This tree is particularly useful for the search for gluino pair production described in the text. The di-sparticle production frame is denoted PP. Intermediate decay states are labeled C. (c) Strong sparticle production with ISR decay tree for use with small mass splitting spectra. CM refers to the center-of-mass of the whole reaction. A signal sparticle system S decays into visible particles (V) and a system of invisible particles (I) that recoil from a jet radiation system ISR.
When the decay tree shown in Fig. 2(b) is used to analyze events, each of the groups V a and V b are further subdivided, with each group undergoing exactly the same partitioning algorithm (based on selecting the combination maximizing the scalar sum of the momentum of the two partitions), resulting in a finer partition with subgroups V 1a=2a and V 1b=2b . Similarly, the same algorithm is used to decide which jets are assigned to the groups V and ISR when analyzing events according to the decay tree shown in Fig. 2(c), where the E miss T , represented as I, is treated as an additional, massless jet in the partitioning algorithm. The reconstruction code for the algorithm can be found in Ref. [87].
The remaining unknowns in the event are associated with the two collections of weakly interacting particles: their masses, longitudinal momenta, and information about how the two groups contribute to the ⃗ E miss T . The RJR algorithm determines these unknowns through subsequent minimizations of the intermediate particle masses appearing in the decay tree. In each of these newly constructed rest frames, all relevant momenta are defined and can be used to construct any variable-multiobject invariant masses, angles between objects, etc. The primary energy-scalesensitive observables used in the search presented here are a suite of variables denoted by H. These H variables denote hemispheres, with the H suggesting similarities with H T , the scalar sum of visible transverse momenta. However, in contrast to H T , these H variables are constructed using different combinations of objects' momenta, including contributions from the invisible four-momenta, and are not necessarily evaluated in the lab frame, nor only in the transverse plane.
The H variables are labeled with a superscript F and two subscripts n and m, H F n;m . The F represents the rest frame in which the momenta are evaluated. In this analysis, this may be the lab frame, the proxy frame for the sparticle-sparticle frame PP, or the proxy frame for an individual sparticle's rest frame P. The subscripts n and m represent the number of visible and invisible momentum vectors considered, respectively. This means, given the number of visible momentum vectors in the frame, these are summed until only n distinct vectors remain. The choice for which vectors are summed is made by finding jets with smallest mutual four vector dot products, using the minimization procedure described above. The same is done for the invisible system so that only m distinct vectors remain. For events with fewer than n visible objects, the sum only runs over the available vectors. The additional subscript "T" can denote a transverse version of the variable, where the transverse plane is defined in a frame F as follows: The Lorentz transformation relating F to the lab frame is decomposed into a boost along the beam axis, followed by a subsequent transverse boost. The transverse plane is defined to be normal to the longitudinal boost. In practice, this is similar to the plane transverse to the beam line.
The variables that are used to define the signal and control regions are listed below. As few requirements are placed on dimensionful variables as possible, in order to increase the generality of the signal regions' sensitivity. Additional discrimination is achieved through a minimal set of dimensionless variable requirements with selections imposed on unitless quantities exploiting common massindependent features of the signals considered.
To select signal events in models with squark pair production, the following variables are used: (i) H PP 1;1 : scale variable as described above. Measures the momentum of missing particles in the PP frame and behaves similarly to E miss T . (ii) H PP T2;1 : scale variable as described above. Behaves similarly to effective mass, m eff (defined as the scalar sum of the transverse momenta of the two leading jets and E miss T ) for squark pair production signals with two-jet final states. (iii) H PP 1;1 =H PP 2;1 : provides additional information in testing the balance of the two scale variables, where in the denominator the H PP 2;1 is no longer solely transverse. This provides excellent discrimination against unbalanced events where the large scale is dominated by a particular object p T or by high E miss T . (iv) p lab PP;z =ðp lab PP;z þ H PP T2;1 Þ: compares the z-momentum of all the objects associated with the PP system in the lab frame (p lab PP;z ) to the overall transverse scale variable considered. This variable tests for significant boost in the z direction.
(v) p PP Tj2 =H PP T2;1 : the ratio of the p T of the second leading jet, evaluated in the PP frame (p PP Tj2 ) to the transverse scale variable, with small values generally more backgroundlike. For signal topologies with higher jet multiplicities, there is the option to exploit the internal structure of the hemispheres by using a decay tree with an additional decay. For gluino pair production, the tree shown in Fig. 2 : represents the fraction of a hemisphere's overall scale due to the second-highest-p T jet (in the PP frame) compared to the overall scale, independently for each hemisphere. The smaller of the values in the two hemispheres is used, corresponding to the index i.
(vii) max i (H P i 1;0 =H P i 2;0 ): testing balance of solely the jets momentum in a given hemisphere's approximate sparticle rest frame (P i , index i indicating each hemisphere) provides additional discrimination against a small but otherwise signal-like subset of background events with a vector boson and associated jets. In order to reject events where the E miss T results from mismeasurements of jets, the E miss T is attributed to one or more jets using a transverse clustering scheme. The transverse components of reconstructed jet four vectors and the E miss T , treated as massless, are organized into a binary decay tree by choosing associations through the recursive minimization of subgroup masses at each decay step using the previously described algorithm. The jet(s) appearing in the decay step where the E miss T appears alone are those that have the smallest inner product with the system of invisible particles in the event, and their mutual transverse momentum is compared with the E miss T using the ratio R QCD : where ⃗p jets T is the transverse momentum of the E miss T associated jet(s) or system of jets in the lab frame. Alternatively, the magnitude and direction of these jets can be compared with the E miss T by considering the "decay angle" of the jetðsÞ=E miss T system, cosðϕ j;E miss T Þ, defined using the transverse jet(s) and E miss T four vectors of the binary decay tree. These quantities are combined into a discriminant Δ QCD , defined as This observable is used to quantify the likelihood that mismeasurements of these jets were responsible for the E miss T . Multijet events with severe jet mismeasurements tend to have Δ QCD values in the interval ½−1; 0 while events with E miss T from weakly interacting particles are more likely to have values in the interval [0,1].
In addition to trying to resolve the entirety of the signal event, it can be useful for sparticle spectra with smaller mass splittings and lower intrinsic E miss T to instead select events with a partially resolved sparticle system recoiling from a high-p T jet from initial-state radiation. To target such topologies, a separate tree for compressed spectra is shown in Fig. 2(c). This tree is somewhat simpler and attempts to identify visible (V) and invisible (I) systems that are the result of an intermediate state corresponding to the system of sparticles and their decay products (S). As the E miss T is used to choose which jets are identified as ISR, a transverse view of the reconstructed event is used which ignores the longitudinal momentum of the jets. The reference frames appearing in the decay tree shown in Fig. 2(c), such as the estimate of the center-of-mass frame (CM), are then approximations in this transverse projection. This tree yields a slightly different set of variables: (i) p CM TS : the magnitude of the vector-summed transverse momenta of all S-associated jets (j ⃗p CM TS j) and E miss T evaluated in the CM frame.
TS =p CM TS : serves as an estimate of mχ=mg =q . This is the fraction of the momentum of the S system that is carried by its invisible system I, with momentum ⃗p CM I in the CM frame. As p CM TS grows it becomes increasingly hard for backgrounds to possess a large value in this ratio-a feature exhibited by compressed signals. (iii) M TS : the transverse mass of the S system. (iv) N V jet : number of jets assigned to the visible system (V) and not associated with the ISR system.
(v) Δϕ ISR;I : the azimuthal opening angle between the ISR system and the invisible system in the CM frame.

VII. EVENT SELECTION AND SIGNAL REGIONS DEFINITIONS
Following the event reconstruction described in Sec. IV, in both searches documented here, events are discarded if a baseline electron or muon with p T > 7 GeV remains, or if they contain a jet failing to satisfy quality selection criteria designed to suppress detector noise and noncollision backgrounds (described in Sec. IV). Events are rejected if no jets with p T > 50 GeV are found. The remaining events are then analyzed in two complementary searches, both of which require the presence of jets and significant missing transverse momentum. The selections in the two searches are designed to be generic enough to ensure sensitivity in a broad set of models with jets and E miss T in the final state. In order to maximize the sensitivity in the mg; mq plane, a variety of signal regions are defined. Squarks typically generate at least one jet in their decays, for instance through q → qχ 0 1 , while gluinos typically generate at least two jets, for instance throughg → qqχ 0 1 . Processes contributing tõ qq andgg final states therefore lead to events containing at least two or four jets, respectively. Decays of heavy SUSY and SM particles produced in longerq andg decay cascades (such as those involving chargino production with subsequent decays e.g.,χ AE 1 → qq 0χ0 1 ) tend to further increase the jet multiplicity in the final state. To target different scenarios, signal regions with different jet multiplicity requirements (in the case of Meff-based search) or different decay trees (in the case of RJR-based search) are assumed. The optimized signal regions used in both searches are summarized in the following.
A. The jets + E miss T

Meff-based search
Due to the high mass scale expected for the SUSY models considered in this study, the 'effective mass', m eff [88], is a powerful discriminant between the signal and SM backgrounds. When selecting events with at least N j jets, m eff ðN j Þ is defined to be the scalar sum of the transverse momenta of the leading N j jets and E miss T . Requirements placed on m eff ðN j Þ and E miss T form the basis of the Meffbased search by strongly suppressing the multijet background where jet energy mismeasurement generates missing transverse momentum. The final signal selection uses a requirement on m eff ðinclÞ, which sums over all jets with p T > 50 GeV and E miss T to suppress SM backgrounds, which tend to have low jet multiplicity.
Twenty-four inclusive SRs characterized by increasing the minimum jet multiplicity, from two to six, are defined in Table II: eight regions target models characterized by the squark pair production with the direct decay of squarks, seven regions target models with gluino pair production followed by the direct decay of gluinos, and nine regions target squark pair or gluino pair production followed by the one-step decay of squarks/gluinos via an intermediate chargino or neutralino. Signal regions requiring the same jet multiplicity are distinguished by increasing the threshold of the m eff ðinclÞ and E miss requirements. This ensures the sensitivity to a range of sparticle masses for each decay mode. All signal regions corresponding to the Meff-based approach are labeled with the prefix "Meff." For SRs with a low number of hard jets, E miss T = ffiffiffiffiffiffi ffi H T p is found to be more discriminant than E miss T =m eff ðN j Þ.
In each region, different requirements are applied for jet momenta and pseudorapidities. These thresholds are defined to reduce the SM background while keeping high efficiency for targeted signal events. Signal regions with high m eff ðinclÞ thresholds are optimized for large mass differences, leading to hard jets in the central region of the detector. For the SRs Meff-2j-2100, Meff-3j-1300 (and Meff-5j-1700) that are optimized for small mass differences betweenq (g) andχ 0 1 , a very high p T threshold is applied to the leading jet in order to explicitly tag a jet originating from initial-state radiation, which results in asymmetric p T requirements on the leading jet and the other jets.
Two signal regions, Meff-2jB-1600=2400, optimized for one-step decay models are designed to improve the sensitivity to models with the cascade squark decay viã χ AE to qWχ 0 1 [ Fig. 1 2 ) is nearly degenerate in mass with the squarks or the gluino. These signal regions place additional requirements on the mass of the large-radius jets to select the candidate hadronically decaying W or Z bosons that, due to the small mass difference between the parent SUSY particles and intermediate chargino or neutralino, can have significant transverse momentum and appear as a single high-mass jet. The signal regions Meff-5j-2000/2600 target similar models and have similar E miss T = ffiffiffiffiffiffi ffi H T p and m eff ðinclÞ selections to the 2jB signal regions, filling the coverage gaps between the 2jB SRs and the other nonboosted SRs. In the other regions with at least four jets in the final state, jets from signal processes are distributed isotropically. Additional suppression of background processes is based on the aplanarity variable, which is defined as A ¼ 3=2λ 3 , where TABLE II. Selection criteria and targeted signal models from Fig. 1 used to define signal regions in the Meff-based search, indicated by the prefix Meff. The first block of SRs targets Fig. 1(a); the second block of SRs targets Fig. 1(d). The third and fourth blocks of SRs target Figs. 1(b) and 1(e). Each SR is labeled with the inclusive jet multiplicity considered (2j, 3j etc.) together with the m eff requirement. The E miss T =m eff ðN j Þ cut in any N j -jet channel uses a value of m eff constructed from only the leading N j jets [m eff ðN j Þ]. However, the final m eff ðinclÞ selection, which is used to define the signal regions, includes all jets with p T > 50 GeV. Large-radius reclustered jets are denoted by large-R j.  (Table continued) λ 3 is the smallest eigenvalue of the normalized momentum tensor of the jets [89].
To reduce the background from multijet processes, requirements are placed on two variables: Δϕðjet; ⃗ EÞ min and E miss T =m eff ðN j Þ. The former is defined to be the smallest azimuthal separation between ⃗ E miss T and the momentum vector of any of the reconstructed jets with p T > 50 GeV. The exact requirements, which depend on the jet multiplicity in each SR, are summarized in Table II, where the criteria for all the Meff-based signal regions can also be found.
B. The jets + E miss T

RJR-based search
The procedure adopted is such that, as the mass splitting between parent sparticle and the LSP increases, the criteria applied to the scale variables are tightened, while the criteria for dimensionless variables are loosened. In searching for the squark pair production, the overall balance of the events is studied with H PP 1;1 =H PP 2;1 . The range selected in this ratio rejects those events where the missing transverse momentum dominates the scale (upper bound) and ensures the sufficient balance between the scales of visible and invisible particles (lower bound). The selection on the p PP Tj2 =H PP T2;1 ratio serves to ensure that each of the jets contributes to the overall scale significantly. This particular ratio is a powerful criterion against imbalanced events with TABLE III. Selection criteria and targeted signal model from Fig. 1 used to define signal regions in the RJR-based search, indicated by the prefix RJR. Each SR is labeled with the targeted SUSY particle or the targeted region of parameter space, such that S, G, and C denote search regions for squark pairs, gluino pairs, or compressed spectra, respectively. W=Z þ jets, where one of the jets has a much higher momentum than the subleading jet. For signals of gluino pair production, the same principles are followed. Tight requirements are placed on H PP 1;1 =H PP 4;1 and H PP T4;1 =H PP 4;1 to target scenarios with more compressed spectra. A selection is applied to the ratio p lab PP;z =ðp lab PP;z þ H PP T4;1 Þ to test the size of the total z-component of momentum relative to the overall scale, requiring that it should be small. A lower bound is placed on p PP Tj2 =H PP T2;1 . This provides a very strong constraint against events where the two hemispheres are well balanced but one of the jets dominates the scale variable contribution. In order to reject events where the E miss T results from mismeasurements of jets, a requirement on the variable Δ QCD is applied, rejecting events where this is deemed likely.
Additionally, separate SRs are defined for models with extremely compressed spectra. Following the pattern of successive SRs targeting larger mass splitting scenarios, several regions designed to be sensitive to various mass splittings utilize the ISR-boosted compressed decay tree described in Sec. VI. These regions target mass splittings between parent squarks and gluinos andχ 0 1 from roughly 25 to 200 GeV.
The selection criteria of the resulting 19 signal regions are summarized in Table III. The entries for jη j1;j2 j and jη j1;2;a;b j correspond to upper bounds on the pseudorapidities of the leading two jets in each event and the leading two jets in each hemisphere a, b, respectively, while jη jV j corresponds to the jets associated with the system V. All signal regions included in the RJR-based search have an RJR prefix.

C. Meff-based and RJR-based signal region comparison
Even though the selection requirements that define the Meff-based and RJR-based SRs use different sets of kinematic observables, the regions are not necessarily orthogonal. The fraction of events common to different regions, for both the SM backgrounds and the SUSY signals, reflects the complementarity of using these two approaches. For models with largeq=g masses, the signal efficiency is prioritized due to low production cross sections. In these cases, stringent requirements on the similarly behaving m eff and H PP T2;1 =H PP T4;1 variables result in a larger overlap between the Meff-based and RJR-based signal regions. Conversely, signal regions designed for increasingly compressed mass spectra have looser m eff and H PP T2;1 =H PP T4;1 , and backgrounds must be suppressed with other, complementary, kinematic requirements. As these additional kinematic observables can be quite different between Meff-based and RJR-based approaches, the orthogonality of these respective SRs increases with decreasing sparticle mass splittings.
This behavior can be observed in Fig. 3, which shows the fractional overlap of selected events in data between the Meff-based and RJR-based SRs. Each of the axes listing the various SRs are organized in the same order, with SRs targeting compressed mass spectra in the lower left of the figure, followed by squark regions with increasing sparticle masses, and then gluinos with increasing mass. This ordering results in a diagonal pattern of larger overlap, as SRs targeting the same signals are more similar. The SRs searching for evidence of squark production (RJR-Sx and Meff-2j-x) have fractions of overlapping events between 25% and 45%, while those targeting gluino production (RJR-Gx and Meff-4j-x) have smaller intersections, ranging from a few percent to 35%. This decrease in overlap for gluino SRs follows from increasing differences between the selections used in the Meff-based and RJR-based approaches. While observables such as E miss T =m eff ðN j Þ and aplanarity are sensitive to global event properties, the RJR-based analysis for gluinos attempts to decompose the event into two hemispheres representing each gluino. Kinematic variables used in the definitions of SRs are calculated from each hemisphere independently, providing complementarity to those describing the total event. Using this additional information in the RJR-based selections leads to generally tighter SRs, adding increased sensitivity for intermediate mass splittings.
Similar trends in event overlaps between SRs are expected for signal contributions, as shown in Figs. 4(a) and 4(b) where a simulated squark signal with mq ¼ 1.5 TeV and masslessχ 0 1 , and a gluino signal with mg ¼ 2 TeV and masslessχ 0 1 are used as examples. In these cases, the SRs targeting squarks and gluinos share a large RJR-S1a RJR-S1b fraction of their events, with the RJR-S4 and Meff-2j-2800 regions best suited to this squark signal having 45% of selected events in common and the analogous gluino SRs (RJR-G4 and Meff-4j-3000) having an overlap of 40%. In the case of a squark signal, the largest overlap of 65% is seen with the RJR-S2a and Meff-2j-1600, with smaller overlap between tighter SRs favored for this signal point.
The RJR-Cx SRs targeting signals with the most compressed mass spectra (0 < mq =g − m˜χ0 1 ≲ 200 GeV) are the most dissimilar from their Meff-based analogs. They attempt to explicitly identify the strong initial-state radiation system that provides the escapingχ 0 1 pair the E miss T needed to satisfy trigger and selection requirements and use kinematic requirements based on this interpretation of the event. The Meff-based SRs designed for these signals (Meff-2j-2100/3j-1300/5j-1700) exploit this compressedmass-spectra event topology by requiring large E miss T = ffiffiffiffiffiffi ffi H T p or large E miss T =m eff ðN j Þ and a hard leading jet corresponding to the ISR system, and the modest m eff requirements result in SRs with relatively large expected background yields and low systematic uncertainties. The RJR-Cx SRs take a more restrictive approach, using observables designed specifically for this ISR event topology, with the corresponding SRs having much lower event yields, higher signal-to-background ratios, but larger uncertainties. This results in much smaller event overlap for both signal and background, as seen in Figs. 4(c) and 4(d) for an example simulated squark signal with mq ¼ 700 GeV and These selected signal points are near the limit of expected sensitivity for these SRs. Meff-based SRs are listed along the x axis with RJR-based regions on the y axis. The intersection events falling in each pair of regions, normalized by the union, is shown on the z axis. The Meff-and RJR-based SRs best suited to each signal, respectively, are indicated by dashed red boxes.

m˜χ0
1 ¼ 600 GeV, and a gluino signal with mg ¼ 1 TeV and m˜χ0 1 ¼ 800 GeV. For these signals, the overlap between the best-suited SRs (RJR-C3 and Meff-3j-1300 for the squark signal, RJR-C5 and Meff-5j-1700 for the gluino) is only about 10%. On the other hand, 65% (35%) of the signal events in RJR-C3 (RJR-C4) are also selected in Meff-3j-1300 (Meff-5j-1700). The more stringent selection strategy employed in the RJR-Cx regions leads to increased sensitivity for compressed mass spectra for each of the signal variants considered in this analysis.

VIII. BACKGROUND ESTIMATION
Standard Model background processes contribute to the event counts in the signal regions. The largest backgrounds in both searches presented here are Z þ jets, W þ jets, top quark pair, single top quark, diboson, and multijet production. Noncollision backgrounds are negligible.
Generally, the largest background results from an irreducible component of Z þ jets events in which Z → νν decays generate large E miss T . Similarly, most of the W þ jets background is composed of W → τν events in which the τlepton decays to hadrons, with additional contributions from W → eν; μν events in which no baseline electron or muon is reconstructed, with E miss T due to neutrinos. Top quark pair production, followed by semileptonic decays, in particular tt → bbτνqq 0 (with the τ-lepton decaying to hadrons), as well as single-top-quark events, can also generate large E miss T and satisfy the jet and lepton-veto requirements. Each of these primary backgrounds is estimated using dedicated control regions, as described in the following section, while diboson production is estimated with MC simulated data normalized using NLO cross section predictions, as described in Sec. III.
The multijet background in the signal regions is due to missing transverse momentum from misreconstruction of jet energies in the calorimeters, jets misidentified as electrons, jets lost due to the JVT requirement, as well as neutrinos from semileptonic decays of heavy-flavor hadrons. After applying the requirements based on Δϕðjet; ⃗ EÞ min and E miss T =m eff ðN j Þ in the Meff-based search, or Δ QCD , p PP Tj2 =H PP T2;1 and Δϕðjet; ⃗ EÞ min in the RJR-based search, as indicated in Tables II and III, the remaining multijet background is negligible.

A. Control regions
In order to estimate the expected background yields, control regions are defined for each of the signal regions in four different final states. In the Meff-based search, each SR has its own set of four CRs, while in the RJR-based search, a common set of CRs is used for all SRs in every targeted signal category (RJR-S, RJR-G or RJR-C). The CR selections are optimized to maintain adequate statistical precision while minimizing the systematic uncertainties arising from the extrapolation of the CR event yield to estimate the background in the SR. The latter is addressed through the fact that the jet p T thresholds and m eff ðinclÞ selections in the CRs are the same as those used for the SR in the Meff-based search. In the RJR-based search, requirements on discriminating variables are chosen to match those used in the SRs as closely as possible. The basic CR definitions in both searches are listed in Table IV.
The γ þ jets region in both searches (labeled as Meff/ RJR-CRγ in Table IV) is used to estimate the contribution of Zð→ ννÞ þ jets background events to each SR by selecting a sample of γ þ jets events with p T ðγÞ > 150 GeV and then treating the reconstructed photon as invisible in the E miss T calculation. For p T ðγÞ significantly larger than m Z the kinematic properties of such events strongly resemble those of Z þ jets events [90]. In order to reduce the theoretical uncertainties associated with the Z=γ Ã þ jets background predictions in SRs arising from the use of LO γ þ jets cross sections, a correction factor is applied to the Meff/RJR-CRγ events as a function of the requirement on the number of jets. This correction factor, κ, ranges from 1.41 to 2.26 for two to six jets, and is determined by comparing Meff-CRγ observations with those in a highly populated auxiliary control region defined by selecting events with two electrons or muons for which TABLE IV. Summary of CRs for the Meff-based and RJR-based searches. Also listed are the main targeted SR backgrounds in each case, the process used to model the background, and the main CR requirement(s) used to select this process. The transverse momenta of high-purity leptons (photons) used to select CR events must exceed 27 (150) GeV. The jet p T thresholds and m eff ðinclÞ selections match those used in the corresponding SRs of the Meff-based search. For the RJR-based search, selections are based on the discriminating variables used in the SRs, as described in the text.  Table IV) aim to select samples rich in Wð→ lνÞ þ jets and semileptonic tt background events, respectively. They use events with one highpurity lepton with p T > 27 GeV and differ in their number of b-jets (zero or ≥ 1, respectively). In both searches, the requirement on the transverse mass m T formed by the E miss T and a selected lepton is applied, as indicated in Table IV. The lepton is treated as a jet with the same momentum to model background events in which a hadronically decaying τ-lepton is produced. This estimation procedure is used to try to get a better idea of the Wð→ lνÞ þ jets and tt cross section in a restricted kinematic phase space, by normalizing the MC to the data for the electron and muon channels, respectively. The propagation of the number of background events from the control region to the signal region is done purely by Monte Carlo which takes into account the impact of all the differences in selection criteria between the control and signal regions. The Meff-CRW and Meff-CRT criteria omit the SR selection requirements on jη jet j, Δϕðjet; ⃗ EÞ min and aplanarity for all SRs, while for the SRs requiring m eff ðinclÞ > 2200 GeV the requirements on E miss T =m eff ðN j Þ are not applied. This is done in order to increase the number of CR data events without significantly increasing the theoretical uncertainties associated with the CR-to-SR extrapolation in the background estimation procedure.

CR
The multijet background in both searches is estimated using a data-driven technique [90], which applies a resolution function to well-measured multijet events in order to estimate the impact of jet energy mismeasurement and heavy-flavor semileptonic decays on E miss T and other variables. The resolution function of jets is initially estimated from MC simulation by matching "truth" jets reconstructed from generator-level particles including muons and neutrinos to detector-level jets with ΔR < 0.1 in multijet samples, and then is modified to agree with data in dedicated samples to measure the resolution function. The Meff-CRQ region uses reversed selection requirements on Δϕðjet; ⃗ EÞ min and on E miss T =m eff ðN j Þ (or E miss T = ffiffiffiffiffiffi ffi H T p where appropriate) to produce samples enriched in multijet background events.
In the RJR-based search, all CRs corresponding to RJR-S (RJR-G) SRs are required to satisfy H PP 1;1 > 800 ð700Þ GeV. Additionally, H PP T2;1 > 1000 GeV (for RJR-S), H PP T4;1 > 1200 GeV (for RJR-G), and M TS > 0 (for RJR-C) are required for RJR-CRW, RJR-CRT and RJR-CRQ regions. In RJR-CRW and RJR-CRT, the requirements on all the other variables used for the RJR-SR selections are chosen such that the loosest value in the SR category (RJR-S, RJR-G, or RJR-C) indicated in Table III is    search. This behavior follows from the simulated top MC samples exhibiting generally harder kinematics than observed in data, as seen in Figs. 6(d) and 7(d). The normalization factors for W þ jets and Z þ jets processes are generally stable with changing kinematic selections but with a clear indication that they become systematically smaller with increasingly strict requirements on the jet multiplicity. This is due to the MC simulation  Table II, except those on the plotted variable. No selection requirements on Δϕðjet; ⃗ EÞ min are applied in Meff-CRW and Meff-CRT regions. The arrows indicate the values at which the requirements on m eff ðinclÞ are applied. The histograms show the MC background predictions, normalized using cross section times integrated luminosity and the dominant process in each CR is normalized using data. In the case of the γ þ jets background, a κ factor described in the text is applied. The last bin includes overflow events. The hatched (red) error bands indicate the combined experimental, MC statistical and theoretical modeling uncertainties. predicting jet multiplicities higher than observed in data events.
Example m eff ðinclÞ distributions in control regions associated with Meff-4j-2200 selections are shown in Fig. 6. Figure 7 shows the p CM TS discriminating variable distributions in control regions corresponding to RJR-C1 signal region selections. In all CRs, the data distributions are consistent with the MC background prediction within uncertainties after normalizing the dominant process in each CR.
Observed p CM TS distribution in control regions (a) RJR-CRγ, (b) RJR-CRQ, (c) RJR-CRW, and (d) RJR-CRT after selecting events for the corresponding control regions as explained in the text for RJR-C1 region and after applying all selection requirements except those on the plotted variable. The arrows indicate the values at which the requirements are applied. The histograms show the MC background predictions, normalized using cross section times integrated luminosity and the dominant process in each CR is normalized using data. In the case of γ þ jets background, a κ factor described in the text is applied. The last bin includes overflow events. The hatched (red) error bands indicate the combined experimental, MC statistical and theoretical modeling uncertainties.

B. Validation regions
The background estimation procedure is validated by comparing the numbers of events observed in the VRs to the corresponding SM background predictions obtained from the background-only fits. Several VRs are defined in both searches, with requirements distinct from those used in the CRs and that maintain low expected signal contamination. Like the CRs, the majority of the VRs are defined in final states with leptons and photons, allowing the different expected background contributions to the SRs to be validated almost separately with high-purity selections.
The Meff/RJR-CRγ estimates of the Zð→ ννÞ þ jets background are validated using samples of Zð→ llÞ þ jets events selected by requiring high-purity lepton pairs of opposite sign and identical flavor for which the dilepton invariant mass lies within 25 GeV of the Z boson mass (Meff/RJR-VRZ). In Meff/RJR-VRZ regions, the leptons are treated as contributing to E miss T . Additional VRs designed to validate the Zð→ ννÞ þ jets estimate in the RJR-based search are also used: the VRZc region, which selects events with no leptons but inverts the Δϕ ISR;I requirement of the SR selection (Table III) and VRZca, which further loosens some other criteria to match the RJR-CRW and RJR-CRT regions. The VRZc regions have a purity of Zð→ ννÞ þ jets of 50%-70%. In order to increase yields in the dilepton final state RJR-VRZ regions, two additional regions, RJR-VRZa and RJR-VRZb are constructed with H PP 1;1 and H PP T2;1 (or H PP T4;1 where appropriate) loosened, respectively, relative to the values used for the RJR-CRW and RJR-CRT regions.
The Meff-CRW and Meff-CRT estimates of the W þ jets and top quark background are validated with the same Meff-CRW and Meff-CRT selections, but applying the Δϕðjet; ⃗ EÞ min requirement and treating the lepton as a jet (Meff-VRW, Meff-VRT). To further validate the extrapolation over the Δϕðjet; ⃗ EÞ min and aplanarity variables from the dedicated W þ jets and top quark CRs to the SRs, additional validation regions Meff-VRWΔΦ and Meff-VRTΔΦ as well as Meff-VRWAp and Meff-VRTAp are defined by relaxing Δϕðjet; ⃗ EÞ min and aplanarity requirements, respectively, relative to Meff-VRW and Meff-VRT.
Similarly, the RJR-CRW and RJR-CRT estimates of the W þ jets and top quark backgrounds are validated using the same selections as for the corresponding CRs, except that the requirements on H PP 1;1 and M TS (RJR-VRWa, RJR-VRTa) or H PP T2;1 and H PP T4;1 (RJR-VRWb, RJR-VRTb) are omitted. Two additional VRs that require the presence of a highpurity lepton and either veto (RJR-VRW) or require the presence of at least one b-jet (RJR-VRT), and require no additional SR selection criteria, are also used in the analysis.
The Meff-CRQ estimates of the multijet background are validated with VRs for which the Meff-CRQ selection is applied, but with the SR E miss where appropriate) and M TS are omitted depending on the region. Additional VRs with inverted Δ QCD (RJR-VRQa), H PP 1;1 (RJR-VRQb) for RJR-S and RJR-G signal regions, and with 0.5 < R ISR < SR requirement (RJR-VRQc) for the RJR-C region (Table III), are also used.

IX. SYSTEMATIC UNCERTAINTIES
Systematic uncertainties in background estimates arise from the use of extrapolation factors that relate observations in the control regions to background predictions in the signal regions, and from the MC modeling of minor backgrounds.
For the backgrounds estimated with MC simulationderived extrapolation factors, the primary common sources of systematic uncertainty are the jet energy scale (JES) calibration, jet energy resolution (JER), theoretical uncertainties, and limited event yields in the MC samples and data CRs. Correlations between uncertainties (for instance between JES or JER uncertainties in CRs and SRs) are taken into account where appropriate.
The JES and JER uncertainties are estimated using the methods discussed in Refs. [75,91,92]. An additional uncertainty in the modeling of energy not associated with reconstructed objects, used in the calculation of E miss T and measured with unassociated charged tracks, is also included. The combined JES, JER and E miss T uncertainty ranges from 1% of the expected background in 2-jet Meff-SRs to 12% in SR Meff-6j-2600. In the RJR-based search, the same uncertainties range from 1% in RJR-C4 to 14% in RJR-G4. Uncertainties in jet mass scale (JMS) and jet mass resolution (JMR) are additionally assigned to SR Meff-2jB-1600 and Meff-2jB-2400, which have requirements on the Signal region RJR-S1a RJR-S1b Relative error  The arrows indicate the values at which the requirements on the plotted variable are applied. When two arrows are shown, these correspond to the looser SR variation "a" and the tighter variation "b." Expected distributions for benchmark signal model points, normalized using NLO þ NLL cross section (Sec. III) times integrated luminosity, are also shown for comparison (masses in GeV). masses of large-radius jets. The JMS uncertainty is estimated using the same methodology as Ref. [93]. A 20% uncertainty is conservatively assigned to the JMR. The combined JMS and JMR uncertainty is 3.2% of the expected background in Meff-2j-1600 and 5.1% in Meff-2j-2400.
Uncertainties arising from theoretical modeling of background processes are estimated by comparing samples produced with different MC generators or by varying the scales. Uncertainties in W=Z þ jets production are estimated by increasing and decreasing the renormalization, factorization and resummation scales by a factor of 2, and by increasing and decreasing the nominal CKKW matching scale, 20 GeV, by 10 and 5 GeV, respectively. Uncertainties in the modeling of top quark pair production are estimated by comparing samples generated with POWHEG-BOX and MG5_aMC@NLO, and by comparing the nominal sample with samples generated using different shower tunes. Uncertainties associated with PDF modeling of top quark pair production are found to be negligible. Uncertainties in diboson production due to PDF, renormalization and factorization scale uncertainties (estimated by increasing and decreasing the scales used in the MC generators by a factor of 2 for all combinations and taking the envelope of them) are accounted for. The combined theoretical uncertainty ranges from 1% in Meff-2j-1200 to 45% in Meff-6j-2600 for Meff SRs. In the RJR-based search, the same uncertainties range from 8% in RJR-S1a to 18% in RJR-G4, with the smaller range largely due to the absence of 6jet SRs. Uncertainties associated with the modeling of Z þ jets production are largest in the 2-jet Meff-SRs (7%). In the RJR-based search, these uncertainties are largest in RJR-S2b and RJR-S3b SR (8%). The impact of lepton reconstruction uncertainties, and of the uncertainties related to the b-tag=b-veto efficiency, on the overall background uncertainty is found to be negligible for all SRs.
The uncertainties arising from the data-driven correction procedure applied to events selected in the CRγ region, described in Sec. VIII, are included in Fig. 9 under "CR statistical uncertainty." Other uncertainties due to CR data sample size range from 4% to 30% for Meff SRs and from 4% to 20% for RJR SRs. The statistical uncertainty arising from the use of MC samples is largest in SRs Meff-6j-2600 (11%) and RJR-G4 (12%). Uncertainties related to the multijet background estimates are taken into account by applying a uniform 100% uncertainty to the multijet yield in all SRs. In most of the SRs these uncertainties are negligible, and the maximum resulting contribution to the overall background uncertainty is less than 1%.
Experimental uncertainties (JES, JER, JMS, JMR, and E miss T ) and MC statistical uncertainty in the SUSY signals are estimated in the same way as for the background and are less than a few percent for most of the signals, except that 7% is assigned as JMS and JMR uncertainties in Meff-2jB-1600 and Meff-2jB-2400. The signal cross section uncertainty is estimated by computing the changes when the renormalization and factorization scale, PDF and the strong coupling constant (α s ) are varied. The uncertainties in the amount of ISR and FSR in the SUSY signals are estimated by varying generator tunes in the simulation as well as scales used in the matrix-element generator as a function of the mass difference, Δm, between gluino (or squark) and χ 0 1 . This uncertainty reaches 20% in the limit of no mass difference and is negligible for Δm > 200 GeV.

X. RESULTS, INTERPRETATION, AND LIMITS
Distributions of m eff ðinclÞ from the Meff-based search for selected signal regions, obtained before the final selections on this quantity (but after applying all other selections), are shown in Fig. 10 for data and the different MC samples normalized using the theoretical cross sections. Similarly, distributions of the final discriminating variables used in the RJR-based search, H PP T2;1 (H PP T4;1 where appropriate) in selected RJR-S and RJR-G regions, and p CM TS in selected RJR-C regions, after applying all other selection requirements except those based on the plotted variable, are shown in Fig. 11. Examples of SUSY signals are also shown for illustration. These signals correspond to the processes to which each SR is primarily sensitive:qq TABLE V. Numbers of events observed in the signal regions used in the Meff-based analysis compared with background predictions obtained from the fits described in the text. The p-values (p 0 ) are the probabilities to obtain a value equal to or larger than that observed in the data. For an observed number of events lower than expected, the p-value is truncated at 0.5. In addition to p-values, the number of equivalent Gaussian standard deviations (Z) is given in parentheses. Also shown are 95% C.L. upper limits on the visible cross section (hϵσi 95 obs ), the visible number of signal events (S 95 obs ), and the number of signal events (S 95 exp ) given the expected number of background events (and AE1σ excursions of the expected number).    VI. Numbers of events observed in the signal regions used in the RJR-based analysis compared with background predictions obtained from the fits described in the text. The p-values (p 0 ) are the probabilities to obtain a value equal to or larger than that observed in the data. For an observed number of events lower than expected, the p-value is truncated at 0.5. In addition to p-values, the number of equivalent Gaussian standard deviations (Z) is given in parentheses. Also shown are 95% C.L. upper limits on the visible cross section (hϵσi 95 obs ), the visible number of signal events (S 95 obs ) and the number of signal events (S 95 exp ) given the expected number of background events (and AE1σ excursions of the expected number).
Signal region RJR-S1a RJR-S1b  (Table continued) production for the lower jet-multiplicity SRs andgg production for the higher jet-multiplicity SRs. In these figures, data and background distributions largely agree within uncertainties. The number of events observed in the data and the number of SM events expected to enter each of the signal regions, determined using the background-only fit, are shown in Tables V and VI and in Fig. 12. The prefit background predictions are also shown in Tables V and VI for comparison.
The background normalizations for each SR are fit to reproduce the event yields observed in the CRs. This is in particular seen in Fig. 5, leading to agreement between data and postfit background predictions in most of the SRs. The most significant observed excess in the signal regions for the Meff-based search, with a p-value for the background-only hypothesis of 0.02, corresponding to a significance of 2.0 standard deviations, occurs in SR Meff-2j-1200 and Meff-2j-2100 (Table V). The most significant observed excess across the signal regions for RJR-based search, with a p-value for the background-only hypothesis of 0.01, corresponding to a significance of 2.5 standard deviations, occurs in SR RJR-S1a (Table VI).
In the absence of a statistically significant excess, limits are set on contributions to the SRs from BSM physics. Upper limits at 95% C.L. on the number of BSM signal events in each SR and the corresponding visible BSM cross section are derived from the model-independent fits described in Sec. V using the CL S prescription. Limits are evaluated using MC pseudoexperiments. The results are presented in Tables V and VI. The model-dependent fits in all the SRs are used to set limits on specific classes of SUSY models using asymptotic formulae [94]. The two searches presented in this paper are combined such that the final observed and expected 95% C.L. exclusion limits are obtained from the signal regions with the best expected CL S value. Fine structures in the limit lines arise due to transitions between best SR's which then also have an impact on the interpolations between grid points.

RJR Signal Region
Data/SM Total In Fig. 13, limits are shown for two classes of simplified models in which only direct production of first-and second-generation mass-degenerate squark or gluino pairs are considered. Limits are obtained by using the signal region with the best expected sensitivity at each point. In these simplified-model scenarios, the upper limit of the excluded first-and second-generation squark mass region is 1.55 TeV assuming masslessχ 0 1 , as obtained from the signal region RJR-S4. The observed exclusion limit is worse than the expected limit in the region with squark (χ 0 1 ) mass of 1 TeV (500 GeV) due to a 2σ excess in SR Meff-2j-1200. The corresponding limit on the gluino mass is 2.03 TeV, if theχ 0 1 is massless, as obtained from the signal region Meff-4j-3000. The best sensitivity in the region of parameter space where the mass difference between the squark (gluino) and the lightest neutralino is small, is obtained from the dedicated RJR-C signal regions. In these regions with very compressed spectra and where the mass difference is less than 50 GeV, squark (gluino) masses up to 650 GeV (1 TeV) are excluded. In Fig. 13(b), the compressed-mass region with a gluino mass below 700 GeV is fully excluded by this analysis; small deviations in the exclusion contour in this region, suggesting nonexcluded areas, are due to interpolation effects. The observed exclusion limit is worse than the expected limit in the region with gluino (χ 0 1 ) mass of 1800 (700) GeV due to a moderate excess (1.3σ) in SR Meff-4j-2200.
In Fig. 14, limits are shown for pair-produced first-and second-generation squarks or gluinos each decaying via an intermediateχ AE 1 to a quark (for squarks) or two quarks (for gluinos), a W boson and aχ 0 1 . Two sets of models of mass spectra are considered for each case. One is with a fixed , the other is with a fixed m˜χ0 1 ¼ 60 GeV. In the former models with squark pair production, mq up to 1.15 TeV are excluded for a masslessχ 0 1 , as is mg up to 1.98 TeV with gluino pair production. These limits are obtained from the signal region RJR-G2b and Meff-6j-2600, respectively. In the regions with very compressed spectra with mass difference between the gluino (or squark) andχ 0 1 less than 50 GeV, RJR-C signal regions also exclude squark (gluino) masses up to 600 GeV (1 TeV). In the latter models, Meff-2jB-1600 and Meff-2jB-2400 extend the limits on squark (gluino) masses up to 1.1 TeV (1.85 TeV) in the regions with small mass difference between the squark (gluino) andχ AE 1 . In Fig. 15, limits are shown for gluino pair production decaying via an intermediateχ 0 2 to two quarks, a Z boson and aχ 0 1 . The mass of theχ 0 1 is set to 1 GeV. In these models, gluino masses below 2.0 TeV are excluded forχ 0 2 masses of ∼1 TeV, as obtained from the signal region Meff-6j-2600.
In Fig. 16, results are presented in the models with mixed decays of intermediateχ AE 1 andχ 0 2 for squark pair and gluino  FIG. 13. Exclusion limits for direct production of (a) first-and second-generation squark pairs with decoupled gluinos and (b) gluino pairs with decoupled squarks. Gluinos (first-and second-generation squarks) are required to decay to two quarks (one quark) and a neutralino LSP. Exclusion limits are obtained by using the signal region with the best expected sensitivity at each point. Expected limits from the Meff-and RJR-based searches separately are also shown for comparison. The blue dashed lines show the expected limits at 95% C.L., with the light (yellow) bands indicating the 1σ excursions due to experimental and background-only theoretical uncertainties. Observed limits are indicated by medium dark (maroon) curves where the solid contour represents the nominal limit, and the dotted lines are obtained by varying the signal cross section by the renormalization and factorization scale and PDF uncertainties. Results are compared with the observed limits obtained by the previous ATLAS searches with jets, missing transverse momentum, and no leptons [11].
pair production. The highest limits on the squark mass are 1.34 TeV and on the gluino mass are 2.02 TeV, which are similar to the models with 100% branching fraction forχ AE 1 (χ 0 2 ) to a W (Z) boson andχ 0 1 . In Fig. 16(b), the limits are extended by the SR Meff-2jet in the region with small mass differences between the gluino andχ 0 2 . In Fig. 17, results are interpreted in simplified pMSSM models assuming only first-and second-generation squarks, gluino andχ 0 1 . Theχ 0 1 is assumed to be purely bino. Models with a fixed m˜χ0 1 ¼ 0; 695; 995 GeV are considered while varying mg and mq. In the limit of high squark mass, gluino masses up to 2 TeV are excluded for masslessχ 0 1 , which is consistent with the simplified models of gluino pair production with decoupled squarks. With a gluino mass of 6 TeV, squark masses up to 2.2 TeV are excluded for a masslessχ 0 1 , much higher than in the simplified models of squark pair production with decoupled gluinos. This is due to the large cross section of squark pair production via gluino exchange diagrams.    FIG. 14. Exclusion limits for direct production of (a),(b) first-and second-generation left-handed squark pairs with decoupled gluinos and (c),(d) gluino pairs with decoupled squarks. Gluinos (first-and second-generation squarks) are required to decay to two quarks (one quark) and an intermediateχ AE 1 , decaying to a W boson and aχ 0 1 . Models with (a),(c) a fixed m˜χAE 1 ¼ ðm˜g þ m˜χ0 1 Þ=2 [or ðmq þ m˜χ0 1 Þ=2] and varying values of m˜g (or mq) and m˜χ0 1 , and (b),(d) a fixed m˜χ0 1 ¼ 60 GeV and varying values of m˜g (or mq) and m˜χAE 1 are considered. Exclusion limits are obtained by using the signal region with the best expected sensitivity at each point. Expected limits from the Meffand RJR-based searches separately are also shown for comparison in (a),(c). The blue dashed lines show the expected limits at 95% C.L., with the light (yellow) bands indicating the 1σ excursions due to experimental and background-only theoretical uncertainties. Observed limits are indicated by medium dark (maroon) curves where the solid contour represents the nominal limit, and the dotted lines are obtained by varying the signal cross section by the renormalization and factorization scale and PDF uncertainties. Results are compared with the observed limits obtained by the previous ATLAS searches with one or no leptons, jets and missing transverse momentum [11,19,95].
A comparison of the Meff-based and RJR-based results highlights some notable features. The RJR-Cx signal regions provide additional sensitivity in the most compressed mass regions beyond their Meff-based counterparts, extending exclusion limits up to 200 GeV inχ 0 1 mass for the smallest mass splitting, as is the case in Fig. 14(a) for firstand second-generation squarks decaying via an intermediatẽ χ AE 1 . In general, the RJR-Cx regions are only mildly sensitive to the specific decays of squarks and gluinos, resulting in similar sensitivity as a function ofq=g andχ 0 1 masses between signal models with direct decays in Fig. 13 and those with intermediate sparticle decays as in Fig. 14.
Despite being largely orthogonal, the RJR-based and Meff-based SRs targeting squark and gluino direct decay signals tend to result in similar sensitivity, with the RJRbased regions generally performing better for intermediate mass splittings. This is the result of tighter restrictions placed on dimensionless variables in the RJR-based regions, resulting in generally lower background yields.
For models with additional jets in the final state expected from intermediate sparticle decays, the Meff-5j-x and Meff-6j-x provide significant additional sensitivity with respect to lower multiplicity SRs, extending exclusion limits by close to 100 GeV in gluino mass when intermediateχ AE 1 decays are considered. These more stringent jet multiplicity requirements compensate for the modest E miss T =m eff ðN j Þ values characteristic of these models.
With requirements aimed at tagging hadronic decays of W=Z bosons, the Meff-2jB-x SRs provide higher  FIG. 16. Exclusion limits for direct production of (a) first-and second-generation left-handed squark pairs with decoupled gluinos and (b) gluino pairs with decoupled squarks. Gluinos (first-and second-generation squarks) are required to decay to two quarks (one quark) and a intermediateχ AE 1 orχ 0 2 with a 50% branching fraction, respectively, withχ AE 1 decays to a W boson and aχ 0 1 , andχ 0 2 decays to a Z or a h boson andχ 0 1 . Models with fixed m˜χ0 1 ¼ 60 GeV are considered while varying m˜g (or mq) and m˜χ0 1 . Exclusion limits are obtained by using the signal region with the best expected sensitivity at each point. The blue dashed lines show the expected limits at 95% C.L., with the light (yellow) bands indicating the 1σ excursions due to experimental and background-only theoretical uncertainties. Observed limits are indicated by medium dark (maroon) curves where the solid contour represents the nominal limit, and the dotted lines are obtained by varying the signal cross section by the renormalization and factorization scale and PDF uncertainties. 2 . Exclusion limits are obtained by using the signal region with the best expected sensitivity at each point. The blue dashed lines show the expected limits at 95% C.L., with the light (yellow) bands indicating the 1σ excursions due to experimental and background-only theoretical uncertainties. Observed limits are indicated by medium dark (maroon) curves where the solid contour represents the nominal limit, and the dotted lines are obtained by varying the signal cross section by the renormalization and factorization scale and PDF uncertainties. Results are compared with the observed limits obtained by the previous ATLAS search in events containing a leptonically decaying Z boson, jets and missing transverse momentum [96]. sensitivity to models with intermediateχ AE 1 andχ 0 2 decays when these sparticles are almost degenerate in mass with their parent squarks and gluinos, corresponding to Figs. 14(b), 14(d), 15, and 16. In these cases, the sensitivity of the Meff-2jB-x regions far surpasses those of the RJR-based and other Meff-based SRs.

XI. CONCLUSION
This paper presents results of two selection strategies to search for squarks and gluinos in final states containing high-p T jets, large missing transverse momentum but no electrons or muons, based on a 36.1 fb −1 dataset of ffiffi ffi s p ¼ 13 TeV proton-proton collisions recorded by the ATLAS experiment at the LHC in 2015 and 2016. No significant deviation from the background expectation is found.
Results are interpreted in terms of simplified models or pMSSM models with only first-and second-generation squarks, or gluinos, together with a neutralino LSP, with the masses of all the other SUSY particles set such that the particles are effectively decoupled. For a massless lightest neutralino, gluino masses below 2.03 TeV are excluded at the 95% confidence level in a simplified model with only gluinos and the lightest neutralino. For a simplified model involving the strong production of squarks of the first and second generations, with decays to a massless lightest neutralino, squark masses below 1.55 TeV are excluded, assuming mass-degenerate squarks of the first two generations. No exclusion is obtained for simplified models of squark (gluino) pair production with lightest neutralino masses above 630 GeV (970 GeV). In simplified models with pairproduced squarks and gluinos, each decaying via an intermediateχ AE 1 to one quark or two quarks, a W boson and aχ 0 1 , squark masses below 1.15 TeV and gluino masses below 1.98 TeV are excluded for masslessχ 0 1 . In pMSSM models assuming squarks, gluinos andχ 0 1 , gluino masses below 2.0 TeV are excluded for a squark mass of 6 TeV or squark masses below 2.2 TeV are excluded for a gluino mass of 6 TeV for masslessχ 0 1 . These results substantially extend the region of supersymmetric parameter space previously excluded by ATLAS searches.