Search for new phenomena with large jet multiplicities and missing transverse momentum using large-radius jets and flavour-tagging at ATLAS in 13 TeV $pp$ collisions

A search is presented for particles that decay producing a large jet multiplicity and invisible particles. The event selection applies a veto on the presence of isolated electrons or muons and additional requirements on the number of b-tagged jets and the scalar sum of masses of large-radius jets. Having explored the full ATLAS 2015-2016 dataset of LHC proton-proton collisions at $\sqrt{s}=13~\mathrm{TeV}$, which corresponds to 36.1 fb$^{-1}$ of integrated luminosity, no evidence is found for physics beyond the Standard Model. The results are interpreted in the context of simplified models inspired by R-parity-conserving and R-parity-violating supersymmetry, where gluinos are pair-produced. More generic models within the phenomenological minimal supersymmetric Standard Model are also considered.


Introduction
As the experiments at the Large Hadron Collider [1] (LHC) continue to amass data from the 13 TeV centreof-mass energy run, observing the production of heavy resonances remains a principal path in the search for physics beyond the Standard Model (SM), such as supersymmetry (SUSY) [2][3][4][5][6][7]. One distinctive signature of such processes would be an increased incidence of events containing a large number of jets accompanied by missing transverse momentum (the magnitude of which is denoted E miss T ). These could originate from extended cascade decays of heavy particles through lighter states, which might interact weakly and therefore have remained unobserved due to their low production cross-sections.
A particle spectrum of this nature is exemplified by the pair production of heavy gluinos (g) that decay via long cascade chains, such as through the superpartners of the electroweak and Higgs bosons. In R-parity-conserving (RPC) [8] SUSY models, these decays culminate in the production of a stable lightest supersymmetric particle (LSP). Cosmological and other observations prohibit an electrically charged or strongly interacting LSP [9][10][11][12], hence the production of these objects, invisible to the detector, would result in missing transverse momentum. Similarly, large jet multiplicities could also be achieved if the gluinos were to decay via on-or off-shell top squarks (t 1 ) or via R-parity-violating (RPV) [13] couplings. In the latter case, the LSP could decay within the detector volume, softening the E miss T spectrum.
Searches by ATLAS were previously reported using smaller quantities of LHC data taken at This paper reports the results of an analysis of 36.1 fb −1 of proton-proton (pp) collision data recorded at √ s = 13 TeV by the ATLAS experiment [14] in 2015 and 2016, scrutinising events that contain significant E miss T and at least seven jets with a large transverse momentum (p T ). Selected events are further classified based on the presence of jets containing B-hadrons (b-jets) or on the sum of the masses of large-radius jets. The b-jet selection improves the sensitivity to beyond-the-SM (BSM) signals with enhanced heavyflavour decays. Given the unusually high jet multiplicities of the target signatures, large jet masses can originate both from capturing the decay products from boosted heavy particles including top quarks and from accidental combinations [15]. A key feature of the search is the data-driven method used to estimate the dominant background from multijet production. Other major background processes include top quark pair production (tt) and W boson production in conjunction with jets (W+jets).
In the next section the ATLAS detector is described, followed by a description of the accumulated data and simulated event samples in Section 3. Then the event reconstruction and selection are explained in Sections 4 and 5. The data-driven method to estimate the multijet background and the estimation of systematic errors are in Sections 6 and 7. The result and interpretations are presented in Section 8 followed by conclusions in Section 9.
The inner-detector system (ID) is immersed in a 2 T axial magnetic field and provides charged-particle tracking in the range |η| < 2.5.
The high-granularity silicon pixel detector covers the vertex region and typically provides four measurements per track. It is followed by the silicon microstrip tracker which usually provides four two-dimensional measurement points per track. These silicon detectors are complemented by the transition radiation tracker, which enables the radial extension of tracks with |η| < 2.0. The transition radiation tracker (TRT) also provides electron identification information based on the fraction of hits (typically 30 in total) above a higher energy-deposit threshold corresponding to the emission of transition radiation.
The calorimeter system covers the pseudorapidity range |η| < 4.9. Within the region |η| < 3.2, electromagnetic calorimetry is provided by barrel and endcap high-granularity lead/liquid-argon (LAr) electromagnetic calorimeters, with an additional thin LAr presampler covering |η| < 1.8, to correct for energy loss in material upstream of the calorimeters. Hadronic calorimetry is provided by the steel/scintillatingtile calorimeter, segmented into three barrel structures within |η| < 1.7, and two copper/LAr hadronic endcap calorimeters. The solid angle coverage is completed with forward copper/LAr and tungsten/LAr calorimeter modules optimised for electromagnetic and hadronic measurements respectively.
The muon spectrometer (MS) comprises separate trigger and high-precision tracking chambers measuring the deflection of muons in a magnetic field generated by superconducting air-core toroids. The precision chamber system covers the region |η| < 2.7 with three layers of monitored drift tubes, complemented by cathode strip chambers in the forward region, where the background is highest. The muon trigger system covers the range |η| < 2.4 with resistive plate chambers in the barrel, and thin gap chambers in the endcap regions.
A two-level trigger system is used to select interesting events [36,37]. The Level-1 trigger is implemented in low-latency electronics and uses a subset of detector information to reduce the event rate to below 90 kHz. This is followed by a software-based High-Level Trigger which reduces the average event rate to about 1 kHz.

Collision data and simulated event samples
Data recorded by ATLAS during 2015 and 2016 are used in this analysis for background estimation as well as in the final signal region (SR) selections. Simulated events produced with several Monte Carlo (MC) event generators provide predictions for subdominant background contributions from SM processes producing top quarks and vector bosons. The main source of background is multijet production, for which predictions are derived directly from data, as described in Section 6.1. Models of potential signals are likewise simulated for analysis optimisation and interpretation of the final results.

Data
Collision events studied for this paper comprise 3.21 ± 0.07 fb −1 recorded with good data quality in 2015 with a further 32.9 ± 1.1 fb −1 recorded during 2016, all with a bunch spacing of 25 ns. The luminosity uncertainty was derived using beam-separation scans, following a methodology similar to that detailed in Ref. [38]. Pile-up, i.e. additional pp interactions in the same or adjacent bunch crossings, contribute to the signals registered by the detector. For this dataset, the average number of interactions per bunch crossing ranged up to 52, with a mean of 22.9.
Events were recorded with a variety of triggers. During both 2015 and 2016, events were selected by a trigger requiring at least six jets with p T > 45 GeV and central pseudorapidity, |η| < 2.4. In addition, in 2015 events were triggered by requiring the presence of at least five jets with p T > 70 GeV, and in 2016 with a trigger requiring at least five jets with p T > 65 GeV and |η| < 2.4.
Minimum data quality requirements are imposed to ensure that only events are used in which the entire ATLAS detector was functioning well. These, for example, exclude data corruption in the ID and calorimeters, excessive noise and spurious jets produced by non-collision backgrounds [39,40].

Simulated event samples
All simulated events were overlaid with multiple pp collisions simulated with the soft QCD processes of P , or using fast simulation based on a parameterisation of the performance of the ATLAS electromagnetic and hadronic calorimeters [46] and on G 4 elsewhere.

Background process simulation
For the generation of tt and single top quarks in the Wtand s-channels P -B v2 [47][48][49][50][51][52] was used with the CT10 PDF sets [53] in the matrix element calculations. Electroweak t-channel single-top-quark events were generated with P -B v1, using the four-flavour scheme for the next-to-leading-order (NLO) matrix element calculations, together with the fixed four-flavour PDF set CT10f4 [53], and with top quark decays using M S [54], preserving all spin correlations. The parton shower, fragmentation, and the underlying event were simulated using P v6.428 [55] with the CTEQ6L1 PDF sets [56] and the Perugia 2012 tune (P2012) [57]. The top quark mass was set to 172.5 GeV. The E G v1.2.0 program [58] was used to model the properties of the bottom and charm hadron decays. Simulated tt events were normalised to the cross-section calculated to next-to-next-to-leading order (NNLO) in perturbative QCD, including soft-gluon resummation to next-to-next-to-leading-logarithm (NNLL) order [59].
Events containing tt and additional heavy particles -comprising three-top, four-top, tt + W, tt + Z and tt + WW production -were simulated at leading order (LO) in the strong coupling constant α S , using M G 5 v2.2.2 [60] with up to two additional partons in the matrix element, interfaced to the P 8.186 parton shower model. The A14 set of P 8 parameters was used [61], together with the NNPDF2.3 LO PDF set [62]. The predicted production cross-sections were calculated to NLO as described in Ref. [60]. In addition, tt + H events were simulated at NLO using M G 5_ MC@NLO v2.2.3 [60], with the NNPDF3.0 NLO PDF set [63]  Diboson processes with four charged leptons, three charged leptons + one neutrino, or two charged leptons + two neutrinos, were simulated using S v2.1.1 [68]. The matrix element calculations contained all diagrams with four electroweak vertices. They were calculated for up to one (for 4 , 2 +2ν) or zero additional partons (for 3 +1ν) at NLO and up to three additional partons at LO using the C and O L matrix element generators and merged with the S parton shower using the ME+PS@NLO prescription. The CT10 PDF set was used in conjunction with dedicated parton shower tuning developed by the S authors. An identical procedure was followed to simulate diboson production with one hadronically decaying boson accompanied by one charged lepton and one neutrino, two charged leptons or two neutrinos, where the calculations included one additional parton at NLO for Z Z → 2 + qq and Z Z → 2ν + qq only, and up to three additional partons at LO.
Theoretical uncertainties were considered for all these simulated samples. By far the most important process simulated in this analysis is tt production, and several samples are compared to estimate the uncertainty in this background. Samples were produced with the factorisation and renormalisation scales varied coherently, along with variations of the h damp parameter in P -B and with parameters set for more/less radiation in the parton shower [69]. Additionally, to account for uncertainties from the parton shower modelling and generator choice, the nominal sample was compared to samples generated with P -B and M G 5_ MC@NLO, interfaced to H ++ [70]. The comparison with samples which vary the amount of additional radiation contributes the largest uncertainty in the signal region predictions.

Supersymmetric signal models
A number of supersymmetric signal model samples are simulated to permit the interpretation of the search results in terms of supersymmetric parameters. Substantial cross-sections are possible for production of gluinos, superpartners of the gluon, whose cascade decays result in a large multiplicity of jets, which may also exhibit an unusually high heavy-flavour content or atypically large masses.
The first is a simplified model, in which gluinos are pair-produced and then decay through an off-shell squark via the cascade:g → q +q +χ where the quarks are only permitted to be from the first two generations. The parameters of the model are the masses of the gluino, mg, and the lightest neutralino, mχ0 1 . The mass of theχ ± 1 is constrained to be (mg + mχ0 1 )/2, and the mass of theχ 0 2 is set to (mχ± 1 + mχ0 1 )/2. A diagram of this "two-step" simplified model is shown in Figure 1(a).
A second type of SUSY model is drawn from a two-dimensional subspace of the 19-parameter phenomenological minimal supersymmetric Standard Model (pMSSM) [75,76], motivated in part by models not previously excluded by the analysis of Ref. [21]. An example pMSSM process is shown in Figure 1(b). These models are selected to have a bino-dominated neutralinoχ 0 1 , kinematically accessible gluinos, and an intermediate-mass Higgsino-dominated multiplet, containing two neutralinos (theχ 0 2 andχ 0 3 ) and a chargino (theχ ± 1 ). The masses of these particles are varied by changing the SUSY soft-breaking parameters M 3 (for the gluino) and µ (for the Higgsinos), while M 1 (for thẽ χ 0 1 ) is held constant at 60 GeV. In order that other SUSY particles remain kinematically inaccessible, the other parameters, defined in Ref. [21], are set to m A = M 2 = 3 TeV, A τ = 0, tan β = 10, to W ± +χ 0 1 . When these decays dominate, they lead to final states with many jets, several of which are b-jets, but relatively little E miss T . This renders this search particularly sensitive compared to most other SUSY searches which tend to require high E miss T . At higher mχ± 1 and lower mg, the decayg → qqχ Gluino-mediated top squark (t 1 ) production, with the squarks being off-shell, is also a good match for the target final state. This scenario is characterised by the pair-production of gluinos followed by their decay with 100% branching ratio to tt +χ 0 1 , through a virtual top squark. Naturalness arguments for supersymmetry favour light gluinos, top squark, and Higgsinos, so this final state is very well motivated. Figure 1(c) shows a diagram for the off-shell process.
Permitting non-zero R-parity-violating (RPV) couplings allows consideration of another variety of gluinomediated top squark production, wherein the last step of the decay proceeds via a baryon-number-violating interaction:t 1 →s +b (charge conjugates implied). Figure 1(d) presents the RPV model. Such R-parityviolating models give rise to final states with low missing transverse momentum. Uniquely among the searches for strongly-produced supersymmetric particles, the current analysis selects final states with sufficiently low missing transverse momentum to be sensitive to these RPV scenarios.
The signal samples were generated using M G 5_ MC@NLO v2.2.2 interfaced to P 8.186 with the A14 tune for the modelling of the parton shower (PS), hadronisation and underlying event. The matrix element (ME) calculation was performed at tree level and includes the emission of up to two additional partons. The PDF set used for the generation was NNPDF23LO. The ME-to-PS matching was done using the CKKW-L prescription [79], with a matching scale set to mg/4.
The gluino-mediated top squark production signal samples were generated with full simulation of the ATLAS detector, whereas the other signal MC samples employed the fast detector simulation.
Signal cross sections are calculated to NLO in the strong coupling constant, adding the resummation of soft gluon emission at next-to-leading-logarithm accuracy (NLO+NLL) [80-84]. The nominal cross section and the uncertainty are taken from an envelope of cross-section predictions using different PDF sets and factorisation and renormalisation scales, as described in Ref.

Primary vertex
Primary vertices are reconstructed using at least two charged-particle tracks with p T > 400 MeV measured by the ID [86]. The primary vertex with the largest sum of squared track transverse momenta ( p 2 T ) is designated as the hard scatter vertex.

Jets
Jets are reconstructed from three-dimensional topological clusters of calorimeter cells (topoclusters) that are noise-suppressed and calibrated to the electromagnetic scale, i.e. corrected for the calorimeter response to electrons and photons [87]. Small-radius jets are built by applying the anti-k t clustering algorithm [88], as implemented in FastJet [89], with jet radius parameter R = 0.4, to the topoclusters. Four-momentum corrections are applied to the jets, starting with a subtraction procedure that removes the average estimated energy contributed by pile-up interactions based on the jet area [90]. This is followed by jet energy scale calibrations that restore the jet energy to the mean response versus particle-level simulation, using a global sequential calibration to correct finer variations due to flavour and detector geometry and finally in situ corrections that match the data to the MC scale [91]. Only jets with p T > 20 GeV and |η| < 2.8 are considered, with the exception of the E miss T calculation, for which jets in the range 2.8 ≤ |η| < 4.5 are also used (see Section 4.6).
To eliminate jets containing a large energy contribution from pile-up, jets are tested for compatibility with the hard scatter vertex with the jet vertex tagger (JVT) discriminant, utilising information from the ID tracks associated with the jet [92]. Any jets with 20 < p T < 60 GeV and |η| < 2.4 for which JVT < 0.59 are considered to originate from pile-up and are therefore rejected from the analysis. Scale factors derived from data are applied for the simulated samples to correct the efficiency of the JVT selection.
A multivariate discriminant (MV2c10) is used to tag jets containing B-hadrons [93]. This exploits the long lifetime, high decay multiplicity, hard fragmentation and large mass of B-hadrons. The selected working point for the b-tagging algorithm [94] tags b-jets in the pseudorapidity range |η| < 2.5 with an efficiency of approximately 70% in simulated tt events, and rejects c-jets, τ-jets and light-quark or gluon jets by factors of of 9.6, 31 and 254, respectively. For the purposes of overlap removal, a loose b-tag designation is defined using a working point with 80% b-tagging efficiency. Where b-tagging selections are applied, efficiency corrections measured in data are applied to simulated events, to improve modelling of the b-tagging efficiencies.
In a second jet formation step [95], small-radius jets with p T > 20 GeV and |η| < 2.0 are reclustered using the anti-k t algorithm with radius parameters R = 1.0 to form large-radius jets. The input jets are required to pass an overlap removal procedure accounting for ambiguities between jets and leptons, as discussed below. In the leptonic control region (CR) defined in Section 5.2, electrons and muons may also be included in the inputs to the jet reclustering provided they satisfy p T > 20 GeV and |η| < 2.0 as for standard jets. Large-radius jets are retained for analysis if they have p T > 100 GeV and |η| < 1.5.

Electrons and photons
Electron and photon candidates are reconstructed from clusters of calorimeter cells defined with fixed rectangular η-φ sizes and then distinguished by matching to ID tracks [96,97]. A multivariate calibration is applied to correct the electron/photon energy scale [98].
Electron candidates are preselected if they have p T > 10 GeV, |η| < 2.47 and pass a "Loose" likelihoodbased quality selection accounting for lateral shower shapes, hadronic shower leakage, 2 hits on tracks, track-cluster matching and the number of high-threshold hits in the TRT. Signal electrons with p T > 20 GeV are defined by requiring a "Tight" likelihood selection including impact parameter restrictions and the "GradientLoose" isolation requirement from Ref. [96] in addition to the preselection. To achieve additional rejection of background electrons from non-prompt sources, signal electron tracks must be matched to the hard scatter vertex with longitudinal impact parameter |z 0 | < 0.5 mm and transverse impact parameter significance |d 0 |/σ(d 0 ) < 5. Corrections to the electron reconstruction and identification efficiency in simulated samples are applied using scale factors measured in data [96].
Photon candidates likewise are identified using tight criteria defined by lateral shower shapes in the first and second layers of the electromagnetic calorimeter, as well as the degree of hadronic shower leakage. Acceptance requirements of p T > 40 GeV and |η| < 2.37 are applied.

Muons
Muon candidates are reconstructed from tracks formed in the ID and MS, which are combined for improved precision and background rejection [99]. Stand-alone muon tracks are used to extend the muon reconstruction coverage beyond the ID acceptance in pseudorapidity (from |η| = 2.5 to |η| = 2.7).
Preselected muons are defined by the "medium" selection of Ref.
[99] using the number of hits on track and track quality and compatibility between the ID and MS measurements. These must have p T > 10 GeV and |η| < 2.7. Signal muons must have a higher transverse momentum, p T > 20 GeV, and satisfy the "GradientLoose" isolation requirement [99], as well as impact parameter matching requirements similar to those for electrons: |z 0 | < 0.5 mm and |d 0 |/σ(d 0 ) < 3. Muon reconstruction and identification efficiencies are corrected with scale factors in simulated samples [100].

Overlap removal
To avoid double counting, a procedure of overlap removal was applied to jets, photons and leptons as follows. The electrons and muons are those passing the preselection.
1. If an electron and a muon share an ID track, the electron is removed and the muon is retained.
2. Photons with ∆R y < 0.4 relative to an electron or a muon are deselected.
3. Any jet that fails the loose b-tag selection is removed if either: • it falls ∆R y < 0.2 from an electron; or • it has no more than three tracks with p T > 500 MeV, or contains an ID track matched to a muon such that p jet T < 2p µ T and the muon track has more than 70% of the sum of the transverse momenta of all tracks in the jet, such that the jet resembles radiation from the muon. 4. Any electrons or muons with ∆R y < 0.4 from a surviving jet are eliminated.
5. Finally, jets that have ∆R y < 0.4 from photons are removed.

Missing transverse momentum
The missing transverse momentum, E miss T , is defined as the magnitude of the negative vector sum of the transverse momenta of preselected electrons and muons, photons and jets, to which is added a "soft term" that recovers the contributions from other low-p T particles [101]. The soft term is constructed from all tracks that are not associated with any of the preceding objects, and that are associated with the primary vertex. In this way, the missing transverse momentum is adjusted for the best calibration of the leptons, photons and jets, while maintaining pile-up independence in the soft term.

Event selection
Target signal events for this analysis are characterised by a large jet multiplicity, beyond what is generated by high-cross-section SM processes, combined with a E miss T that is significantly larger than that expected purely from detector resolution. Several signal regions are defined that select a minimum jet multiplicity and further require a large value of the ratio E miss the sum being restricted to jets with p T > 40 GeV, |η| < 2.8. This ratio is approximately proportional to the significance of the E miss T , under the assumption that the expected E miss T is zero and the resolution of the E miss T originates entirely from the stochastic variation in the jet momentum measurement. For jets with p T 1 TeV, the relative jet resolution scales approximately as 1/ √ p T .
Several auxiliary measurements are carried out in control and validation regions (VR) in order to define and constrain the major backgrounds to the analysis. Events selected at a lower jet multiplicity are used to extract the shape of the E miss T / √ H T distribution, which is then extrapolated to the signal regions to quantify the multijet background, as described fully in Section 6.1. The normalisation of the tt and W+jets background components is adjusted to match data in control regions, using the procedure defined in Section 6.2.

Signal region definitions
The common selection of events for all the signal regions is as follows. To limit the contribution of SM background processes in which neutrinos are produced, leading to significant E miss T , events containing any preselected electron or muon following the overlap removal procedure are rejected.
Biases in the E miss T due to pile-up jets surviving the JVT selection are removed by excluding events for which a jet with 60 < p T < 70 GeV and JVT < 0.59 lies opposite to the E miss 2). Likewise, events are rejected if they contain a jet with p T > 50 GeV and |η| < 2.0 pointing towards regions in which tile calorimeter modules were disabled. These requirements are also applied to the control regions and validation regions described later in Section 5.2.1.
Subsequently, restrictions on the jet multiplicity N jet are imposed, depending on the analysis channel; only jets with p T > 50(80) GeV and |η| < 2.0 are considered as signal jets and therefore used in the N jet selection. These selections are abbreviated as j50 ( j80), for which the corresponding jet multiplicities are denoted N 50 jet and N 80 jet . The lower and higher jet-p T thresholds were optimised to permit sensitivity to a variety of potential SUSY mass spectra.
A threshold of E miss T / √ H T > 5 GeV 1/2 is the last element of the common selection. This criterion eliminates the vast majority of SM multijet and other background events with low E miss T , while retaining sensitivity to a broad range of potential signals.
Next, the SRs in the two channels of the analysis are defined by a further categorisation of events.

Criterion
Heavy-flavour channel Jet mass channel 9, 10, 11 ≥ 7, 8, 9 ≥ 8, 9, 10 Lepton veto No preselected e or µ after overlap removal b-jet selection p T > 50 GeV and |η| < 2.0 Large-R-jet selection p T > 100 GeV and |η| < 1.5 Table 1: Summary of the selection criteria for all signal regions used in this analysis. In each column, the three selection criteria on the number N b-tag of b-tagged jets or the two on the the sum M Σ J of masses of large-radius jets are applied to define separate signal regions for each of the jet multiplicities considered.

Heavy-flavour channel
The following N jet values are considered in this channel: minimum N 50 jet ∈ {8, 9, 10, 11}, and minimum N 80 jet ∈ {7, 8, 9}. Motivated by the desire to achieve good sensitivity to models with differing probabilities of heavy flavour jets being produced during cascade decays, three signal regions that respectively require N b-tag ≥ 0, 1, 2 are defined for each value of N jet , where the b-jets must have p T > 50 GeV and |η| < 2.0.

Jet mass channel
Should sparticles be produced and decay through a long decay chain, or provide enough kinetic energy to significantly boost heavy particles such as top quarks and bosons, signal events might be characterised not only by an unusually large jet multiplicity but also by the formation of large-radius jets with high masses. The kinematic structure of SM events, by contrast, does not produce a high rate of events containing large-radius jets with mass greater than the top quark mass.
For background discrimination in this channel, a selection variable, M Σ J , is defined to be the sum of the masses m R=1.0 j of the large-radius jets where the sum is over the large-radius jets that satisfy p R=1.0 T > 100 GeV and |η R=1.0 | < 1.5, as described in Section 4. Two thresholds for M Σ J at 340 GeV and 500 GeV, chosen following optimisation studies, define signal regions for N 50 jet ∈ {8, 9, 10}, while no j80 SRs are defined. As these thresholds are approximately twice and thrice the top quark mass, the residual irreducible backgrounds are respectively from top quark pair production in association with vector bosons and four-top processes, both of which have a very small rate.
A summary of all signal region selections is given in Table 1.

Control region definitions
For each signal region, three control regions are used to constrain the background predictions using data, and are split into two sets. The first set, referred to as the multijet template region (TR) selection, maintains the same lepton veto as used in the SR, but modifies the signal jet multiplicity or E miss T / √ H T selection. Secondly, a pair of leptonic control regions are defined, classified according to the absence or presence of a b-tagged jet, in which the lepton veto is replaced with a requirement on the presence of exactly one signal electron or muon (henceforth referred to merely as "lepton", ).

Multijet template region
Fundamental to this analysis is the extraction of an estimate of the multijet background directly from data, avoiding large theoretical uncertainties in the inclusive and differential cross-sections for these processes. The full estimation procedure is described in Section 6.1.
Broadly, four different selections are used to evaluate the background prediction and its associated systematic uncertainties. The shape of the full E miss is measured in events containing exactly six signal jets with p T > 50 GeV for the j50 signal regions and exactly five signal jets with p T > 80 GeV for the j80 signal regions. For normalisation of the template prediction, events are counted in a TR defined by the same signal jet multiplicity as the signal region, but an upper bound of 1.5 GeV 1/2 on the E miss T / √ H T variable. Validation regions are defined that require seven signal jets with p T > 50 GeV for the j50 signal regions and six signal jets with p T > 80 GeV for the j80 signal regions, and also impose a minimum E miss T / √ H T > 5 GeV 1/2 threshold, as in the signal regions. Finally, an additional validation region is defined in the range 1.5 < E miss T / √ H T < 4.5 GeV 1/2 , for each signal region jet multiplicity. The same N b-tag and M Σ J thresholds are applied in each template and validation region as in the corresponding signal region.

Leptonic control regions
Also important is the estimation of the next two largest background processes, tt and W+jets, from MC simulation, as detailed in Section 3.2.1. To correct for potential mismodelling of the process cross-sections and kinematics by the event generators, the normalisation for the background predictions is modified based on a simultaneous fit of the auxiliary measurements, explained in Section 6.3.
The leptonic control regions constraining the tt and W+jets normalisation are defined with identical selection criteria as their corresponding signal regions, apart from the following differences, summarised also in Table 2: 1. Instead of rejecting events containing a preselected lepton, events must contain exactly one signal lepton with p T > 20 GeV.
2. To prevent contamination from potential signals, events must satisfy a requirement on the transverse mass m T < 120 GeV, where 3. To increase the number of selected events, the minimum signal jet multiplicity N jet is reduced by one from the corresponding signal region. However, if the lepton satisfies the p T and η requirements imposed on signal jets, then it is treated as a signal jet for the purposes of this selection. This reflects the main mechanism by which tt and W+jets events pass the signal region selection: misidentification of an electron or hadronically-decaying tau lepton as a jet, which can increase the jet multiplicity. Events with leptons which are unreconstructed as they lie outside of detector acceptance can also contribute to the signal regions, but are a subdominant contribution.
4. Events consistent with W+jets and tt production are separated by means of the N b-tag selection; the W+jets CR requires N b-tag = 0 while the tt CR requires N b-tag ≥ 1.
5. The E miss T / √ H T threshold is lowered from 5 GeV 1/2 to 3 GeV 1/2 or 4 GeV 1/2 when it is necessary to increase the statistical precision of the measurement. The E miss T / √ H T thresholds are specified in Table 3.

Control regions
Lepton multiplicity Exactly one signal e or µ Lepton p T > 20 GeV m T < 120 GeV Jet p T , |η| Same as SR Number of jets including lepton N SR  6 Background estimation techniques

Multijet template estimation
Accurate modelling of multijet processes by performing QCD calculations involving high multiplicity multi-leg matrix elements is difficult. This is compounded by the challenges of reproducing events populating the tails of the detector response, representative of the high-E miss T events selected in this analysis. Hence, to confidently estimate the multijet background component, which makes up 50-70% of the total SM expectation, the prediction is based on direct measurements in data.
The strategy used in this analysis is based on the observation that the E miss T / √ H T spectrum for selected multijet events is primarily determined by the calorimeter response to jets, which is approximately independent of how the total jet transverse energy H T is partitioned between the jets. Thus, the E miss T / √ H T spectrum measured in events with a lower jet multiplicity does not greatly differ from that observed in events with a high jet multiplicity. The normalisation of the template is fixed in the range E miss T / √ H T < a such that a < b < c, which is entirely dominated by multijet events. In the template region, the observation in data is denoted n obs , while the predicted number of events with neutrinos is written n MCν .
While the exact division of H T among the multiple jets in a single event does not significantly influence the template independence, the distribution of H T itself is forced higher as the N jet requirements are made more stringent. This implies the existence of an indirect correlation between the E miss T / √ H T and the jet multiplicity, which challenges the earlier assumption of template independence. It is therefore necessary to extract the multijet template in several bins of H T in order to remove the subdominant residual dependence of E miss T / √ H T on H T . The lower bin boundaries are set at 0, 600, 900 and 1200 GeV, which was found to be sufficient to remove the dependence of the template on H T . Predictions for each bin are derived independently and summed to obtain the total SR expectation.
The dependence of the template prediction on pile-up was studied in detail. While the width of the E miss T / √ H T distribution itself shows a correlation with the amount of pile-up, both due to the growth of the jet resolution and the influence of additional jets present in the event, increases in the amount of pile-up do not worsen the closure of the template prediction, i.e. the ability of the method to correctly predict the multijet background in validation regions free of signal. This demonstrates that the template method accurately captures the variation in the E miss T / √ H T spectrum under changing LHC conditions, and that there is no observable bias in the signal region acceptance for a given level of pile-up.
Other potential influences on the closure of the template such as the heavy-flavour composition were also studied carefully. The most important of these effects are kinematic variations between the template and signal regions, and differences in the number of heavy-flavour jets in the two event selections. While no major changes in the prediction were observed in these checks, systematic uncertainties that estimate the sensitivity of the template prediction to these variables are assessed.
Kinematic differences are covered by comparing the nominal estimate to the prediction extracted using an alternative H T -binning strategy, setting the bin boundaries instead at 0, 600, 800, 1000, 1200 and 1400 GeV. The resulting uncertainty is typically 5-10% in the SRs.
An uncertainty due to jet flavour composition is determined as the difference between the nominal estimate, which assumes an identical flavour composition between the TR and SRs, and a χ 2 fit that interpolates between the nominal estimate and a flavour-split template estimate. The flavour-split template prediction is produced by separating the template and signal regions into two bins, one requiring exactly as many b-jets as in the SR N b-tag selection, and the other requiring at least one more. A χ 2 fit to data in the validation regions is then used to linearly combine the nominal and flavour-split templates. The resulting combined template is used as a basis for comparison to the nominal prediction. This procedure ensures that an appropriate uncertainty is estimated if the nominal estimate is significantly different from the best fit; if the naïve flavour-split estimate describes the data poorly, this does not result in an overestimate of the uncertainty. For the jet mass channel, this uncertainty ranges from 3% to 6%. It is larger in the heavy-flavour channel: at most 20% in the tightest selections, and up to 12% elsewhere.
Finally, to account for other potential sources of mismodelling, an overall closure uncertainty is computed. This is defined as the maximal relative difference between the template prediction and the observation in data for the VRs defined in Section 5. Example distributions of E miss T / √ H T in the lower-jet-multiplicity VRs are shown in Figure 2. The degree of closure varies, generally ranging between 8% and 12% and extending to 30% for regions with the fewest events.

Leptonic background estimates
All background contributions from processes in which W → ν or Z → νν decays produce neutrinos, including single or pair production of top quarks and electroweak vector bosons, are estimated using MC simulation. The two largest of these, tt and W+jets, are responsible for 20-45% and up to 10% of the SM background respectively. Other processes, such as Z+jets, single top and diboson production collectively make up no more than 12% of the total SR expectation. As such, corrections to the size of the tt and W+jets background components, together with the multijet template estimate previously described, provide a sufficiently accurate background prediction for this search. For each of the tt, W+jets and multijets background processes, a normalisation factor µ is determined, based on a likelihood fit described in Section 6.3.
Control regions defined as in Section 5.2.2 provide enriched samples of events from the relevant processes, in a kinematic region close to the signal selection. The purity of the CRs is around 85% for tt and typically 25-50% for W+jets. As only these two processes contribute substantially to the CR populations, this level of purity is adequate to constrain the normalisations for both well.
Distributions of the number of jets (p T > 20 GeV, |η| < 2.8) are shown in Figure 3 for a selection of the tt and W+jets CRs.

Combined background fits
For each background process constrained by the fit, an unconstrained normalisation factor µ b , b ∈ {tt, W, multijet} is defined, such that µ b = 1 implies consistency with the nominal MC cross-sections for tt and W+jets. The normalisation factor µ multijet allows the MC subtraction applied in the template estimate to be corrected by the CR measurements, and to be modified coherently with any systematic variations applied to the MC simulation.
A likelihood is then constructed for the ensemble of measurements in the control regions as the product of Poisson distributions whose means are specified by the nominal MC estimate for that region, including the free normalisation factors µ b [102]. For µ tt and µ W , the corresponding leptonic control regions provide the constraints. The 6-jet ( j50) or 5-jet ( j80) template region is treated as another control region in the fit such that µ multijet is coupled to any modifications of µ tt and µ W . If µ tt = µ W = 1, then µ multijet = 1 by construction, as the same region is used to derive the nominal multijet estimate. The systematic uncertainties (see Section 7.1) are implemented in the form of Gaussian-constrained nuisance parameters modifying the Poisson mean of each background component contributing to the estimate in a given signal or control region.
Minimisation of the likelihood (profiling) fixes the values of, and uncertainties in, µ b , which can then be combined with the MC and template predictions to obtain the total background prediction in the signal region. The compatibility of the background prediction and SR observation is computed in the form of a p-value CL b which is the probability of an upwards fluctuation from the SR prediction no larger than that observed in data, given the background model.   The energy/momentum uncertainties affect jets, electrons, muons and photons, and are also propagated to the missing transverse momentum. Jet energy scale and resolution systematic uncertainties contribute 6-12% to the uncertainty in the SR yields. The soft term of the E miss T also has its own associated uncertainties, which in the jet mass channel may have up to an 8% effect. In this category also fall the uncertainty in the total integrated luminosity considered for analysis as well as in the total inelastic pp cross-section, which affects the simulation of pile-up (<1%).

Number of Events / Bin
Theoretical uncertainties in the event generation affect both the background and signal MC samples. These are assessed by varying the matrix element and parton shower generators used, or by modifying scales (renormalisation, factorisation, resummation, matching) involved in the process calculations. Variation in the degree of additional QCD radiation accompanying tt production is the single largest source of uncertainty in the SRs (10-25%); parton shower uncertainties play a subdominant role, typically being half as large as, but occasionally comparable to, the radiation systematic uncertainty. Constant uncertainties of 30% and 50% respectively are applied to the normalisation of diboson production and top quark pair production in association with vector bosons, and have an overall negligible effect on the analysis results.
As described in Section 6.1, uncertainties in the multijet background estimates are assessed, where kinematic and flavour differences between the template and signal regions are considered. An additional overall systematic uncertainty is ascribed for general non-closure of the template prediction. Apart from in the jet mass channel SRs, where the kinematic and flavour uncertainties are at most 3%, and in the most statistically limited SRs, the uncertainties from the three sources are similar in magnitude. Where the statistical precision is poorer, fluctuations can drive the non-closure uncertainty up to 18%.

Hypothesis testing
For the interpretation of the signal region observations, the likelihood fits for background estimation (Section 6.3) are extended to perform two forms of hypothesis tests using a profile-likelihood-ratio test statistic [103], quantifying the significance of any observed excesses or the lack thereof. The discovery test discriminates between the null hypothesis stating that the SR measurement is consistent with only SM contributions and an alternative hypothesis postulating a positive signal. Conversely, any given signal model can be examined in an exclusion test of the signal-plus-background hypothesis, where an observation significantly smaller than the combination of SM and SUSY processes would lead to rejection of the signal model.
Taking into account all background predictions, normalisation factors and systematic uncertainties, the fit is implemented by including the SR in the ensemble of measurements and adding an additional signal component solely in the SR. Using a profile-likelihood-ratio test, the discovery p-value p 0 , corresponding to the probability of an upward fluctuation in the absence of any signal, can be determined. This configuration also permits an upper limit on the visible signal cross-section to be set for an arbitrary signal, where it is assumed that the signal contamination in the control regions is negligible.
Exclusion testing of a chosen signal model proceeds similarly, but a signal component is allowed in all control regions as well as the signal region, to correct for potential signal contamination (which has been verified to be small). Theoretical and experimental systematic uncertainties in the signal MC simulation are included in the fit. A profile-likelihood-ratio test is then made of the compatibility between the best-fit µ signal from data and the nominal signal hypothesis, corresponding to a signal strength µ signal = 1. This provides the exclusion p-value p 1 . Points in the SUSY parameter space are considered excluded if the CL s parameter, computed as p 1 /(1 − CL b ), is smaller than 0.05 [104]. This protects against spurious exclusion of signals due to observing SR event counts significantly smaller than those predicted. While not strictly defining a frequentist confidence level, these are referred to as 95% confidence level CL limits.

Results and interpretation
The expected and observed event counts in the leptonic control regions are evaluated and normalisation factors derived. In general, the tt normalisation is close to one for lower jet multiplicities but may be as small as 0.71 for high jet multiplicities. For µ W , the range is typically 0.3-0.6. Correspondingly, µ multijet is corrected upwards by up to 24%.
Signal region yields as observed in data are summarised in Table 4. These are illustrated graphically in Figure 4. The most significant difference from the SM prediction is a deficit in the 9j MJ500 region with a statistical significance of 1.8σ and a corresponding p-value (1 − CL b ) of 0.04. Similar deficits are observed in the other MJ SRs, but the large overlap between these SRs implies that the deficits are strongly correlated.
The full distributions of E miss T / √ H T are shown for two of the most sensitive signal regions in Figure 5.
For all signal regions, the data agree with the predicted E miss T / √ H T distributions within the systematic uncertainties. Multijet   Table 4: The expected SM background (and separately the multijet and leptonic contributions) and the observed number of data events. The SM background normalisations are obtained from fits to the data in control regions, as described in the text.  Table 5 quantifies the results of the fit to all signal regions. When testing for a positive signal, the smallest p 0 value observed is 0.2, for N 80 jet ≥ 9 and N b-tag ≥ 2. The strongest limits set on the visible cross-section are of about 0.19 fb, for N 50 jet ≥ 11 and N b-tag ≥ 2.

Exclusion limits
Using the exclusion configuration defined in Section 7.2, limits are set at the 95% CL in the signal scenarios described in Section 3.2.2. Constraints from all 27 SRs are combined by considering only the SR with the best expected exclusion sensitivity at each signal model point. These are illustrated in several parameter planes in Figures 6 and 7.
In the mg, mχ± 1 projection of the pMSSM, constraints are set such that mg 1600 GeV is excluded for mχ± 1 < 600 GeV. The limit falls to mg 1360 GeV for mχ± 1 800 GeV.
Limits are set up to mg ≈ 1800 GeV for small LSP masses when considering the simplified model assuming a two-step cascade decay of the gluino. For mg 800 GeV, models are excluded provided that mχ0 1 < 475 GeV. The limits lie in the range 500 < mχ0 1 < 700 GeV as the gluino mass increases to mg = 1600 GeV.
Simplified models of gluino-mediated top squark production are excluded for gluino masses up to 1500 GeV, as long as mχ0 1 600 GeV, when assuming that the squark is more massive than the gluino. When RPC restrictions are relaxed, gluino masses between 625 and 1375 GeV are excluded for 400 < mχ0 1 < 800 GeV in a scenario where the top squarks decay through an RPV coupling tosb.

Conclusion
A search for heavy particles predicted by supersymmetric or other models of physics beyond the SM, that decay to produce large jet multiplicities in association with E miss T , was performed using 36.1 fb −1 of √ s = 13 TeV LHC pp collision data collected by ATLAS in 2015 and 2016. No significant excesses over the Standard Model background were observed in signal regions selecting up to 11 jets with p T > 50 GeV or 9 jets with p T > 80 GeV. The largest-jet-multiplicity event observed in data had 13 jets with p T > 80 GeV, while the greatest observed jet mass sum was M Σ J = 1.3 TeV. Exclusion limits are placed on gluino production in supersymmetric signal scenarios with a range of model assumptions. The tightest limits are set at mg ≈ 1800 GeV in a simplified model assuming a two-step cascade decay via theχ 0 2 andχ ± 1 . A slice of the phenomenological MSSM is excluded for mg < 1360 GeV, with tighter constraints at mg ≈ 1600 GeV for mχ± 1 < 600 GeV. When assuming that the gluino decays through off-shell top squarks, masses of the gluino below 1500 GeV are excluded provided mχ0 1 < 600 GeV. Limits are also set in an R-parity-violating model with baryon-number-violating couplings permittingt 1 →sb, such that the gluino mass must be greater than 1250-1375 GeV when the top squark mass is in the range 400 < mt 1 < 800 GeV.