Search for new phenomena in events with an energetic jet and missing transverse momentum in pp collisions at √s = 13 TeV with the ATLAS detector

Results of a search for new physics in final states with an energetic jet and large missing transverse momentum are reported. The search uses proton-proton collision data corresponding to an integrated luminosity of 139 fb − 1 at a center-of-mass energy of 13 TeV collected in the period 2015 – 2018 with the ATLAS detector at the Large Hadron Collider. Compared to previous publications, in addition to an increase of almost a factor of four in the data size, the analysis implements a number of improvements in the signal selection and the background determination leading to enhanced sensitivity. Events are required to have at least one jet with transverse momentum above 150 GeV and no reconstructed leptons ( e , μ or τ ) or photons. Several signal regions are considered with increasing requirements on the missing transverse momentum starting at 200 GeV. Overall agreement is observed between the number of events in data and the Standard Model predictions. Model-independent 95% confidence-level limits on visible cross sections for new processes are obtained in the range between 736 fb and 0.3 fb. Results are also translated into improved exclusion limits in models with pair-produced weakly interacting dark-matter candidates, large extra spatial dimensions, supersymmetric particles in several compressed scenarios, axionlike particles, and new scalar particles in dark-energy-inspired models. In addition, the data are translated into bounds on the invisible branching ratio of the Higgs boson.


Introduction
This paper presents the results of a new search for new phenomena in events containing an energetic jet and large missing transverse momentum p miss T (with magnitude miss T ) in proton-proton collisions at a centre-of-mass energy √ = 13 TeV recorded by the ATLAS detector at the Large Hadron Collider (LHC). The final-state monojet signature of at least one energetic jet, large miss T and no leptons constitutes a distinctive signature for new physics beyond the Standard Model (SM) at colliders. This signature has been extensively studied at the LHC in the context of searches for large extra spatial dimensions (LED), supersymmetry (SUSY), weakly interacting massive particles (WIMPs) as candidates for dark matter (DM) [1][2][3][4][5], and signals from models inspired by dark energy (DE) with new scalar particles in the final state [6]. In addition, experimental results have been reinterpreted in terms of new theoretical scenarios with axion-like particles [7]. Finally, the monojet final-state results have been used to constrain the invisible branching fraction of the Higgs boson [8,9]. In the following, the different models are discussed briefly. Figure 1 shows diagrams for some of the models. The existence of a non-baryonic form of matter is well established from a number of astronomical observations [10][11][12]. The existence of a new, weakly interacting massive particle is often hypothesized [13], as it can lead to the correct relic density for nonrelativistic matter in the early universe [14] as measured from data from the Planck [15] and WMAP [16] Collaborations. For WIMP masses below 1 TeV, WIMPs may be pair-produced at the LHC. Traditionally, a monojet final state has been considered a golden channel for the discovery of WIMPs at colliders. In this case, the WIMP pair is produced in association with a jet of particles from initial-state radiation, leading to the signature of a jet and missing transverse momentum (see Figure 1(a)). Results are presented for simplified DM models [17][18][19] where Dirac fermion WIMPs ( ) are pair-produced from quarks via -channel exchange of a spin-1 mediator particle ( ) or a spin-0 mediator particle ( ) with axial-vector or pseudoscalar couplings, respectively. In the case of the axial-vector mediator model with couplings of the mediator to WIMPs and SM quarks set to = 1 and = 1/4, respectively, mediator masses below 1. 55 TeV have been already excluded at 95% confidence level (CL) for very light WIMPs in previous analyses [4].
Supersymmetry is a theory of physics beyond the SM which can solve the hierarchy problem in a natural way and can provide candidates for dark matter [20][21][22][23][24][25]. SUSY introduces a new supersymmetric partner (sparticle) for each particle in the SM. Specifically, a new scalar field is associated with each quark chirality state. Two squark mass eigenstates˜1 and˜2 result from the mixing of the scalar fields for a particular flavor. In supersymmetric extensions of the SM that assume R-parity conservation [26][27][28], sparticles are produced in pairs and the lightest supersymmetric particle (LSP) is stable. The LSP is assumed to be the lightest neutralino˜0 1 . The results are interpreted in terms of searches for squark production using simplified models in scenarios for which the mass difference Δ ≡˜−˜0 1 is small (compressed-mass scenario). In this case, the T of the resulting quark jets and the miss T in the final state are both small, making it difficult to reconstruct the SUSY signal. The monojet signature provides unique access to this parameter space, for which the presence of jets from initial-state radiation is used to identify signal events, leading to larger miss T (see Figure 1(b)). In the case of bottom-squark (sbottom) and top-squark (stop) pair production in a compressed-mass supersymmetric scenario, squark masses below about 430 GeV have been already excluded at 95% CL [4].
The origin of the accelerating expansion of the universe [29,30] is, together with the nature of the dark matter, a major open question in cosmology. The theoretical understanding of the accelerating expansion of the universe in terms of fundamental physics, beyond the ad hoc adoption of a cosmological constant in general relativity, often involves the introduction of additional scalars interacting with both the gravity and matter fields [31]. Here an effective field theory implementation of the Horndeski theories [32] is considered [33], introducing a new dark-energy scalar field , governed by an effective mass 2 and a coupling * to matter, which is considered universal. For the model relevant for this case, the new scalar particle is stable and is produced in pairs, leaving the experiment undetected. When they are produced in association with an energetic gluon, it leads to a monojet final-state topology (see Figure 1(c)). Previous results [6] indicate no sensitivity for * ≤ 1.8, and values of 2 below 1.2 TeV have been excluded at 95% CL for * ≥ 3.5.
Large extra spatial dimensions have been postulated to explain the large difference between the electroweak unification scale at (10 2 ) GeV and the Planck scale Pl at (10 19 ) GeV. In the Arkani-Hamed, Dimopoulos, and Dvali (ADD) model of LED [34], the presence of extra spatial dimensions of size leads to a fundamental Planck scale in 4 + dimensions given by Pl 2 , where is the fundamental scale of the 4 + -dimensional theory. The extra spatial dimensions are compactified, resulting in a Kaluza-Klein tower of massive graviton modes (KK graviton). If produced in high-energy proton-proton collisions in association with a jet of hadrons, a KK graviton escaping into the extra dimensions can be inferred from miss T , and can lead to a monojet event signature. Values of below 7.7 TeV at = 2 and below 4.8 TeV at = 6 have been already excluded at 95% CL [4].
New pseudoscalar bosons, referred to as axion-like particles (ALPs), are introduced in different models involving the breaking of additional U(1) symmetries. The existence of axions was postulated [35] in order to address the strong CP problem for which an anomalous global U(1) symmetry is spontaneously broken. Axions are candidates for explaining the dark-matter content of the universe. The strength of the coupling between the axions and the ordinary matter is governed by the electroweak symmetry breaking scale, leading to rather strong constraints. Other models with ALPs, going beyond the minimal QCD axion realization, consider much weaker interactions suppressed by a much higher scale [7,36]. In this paper, an effective implementation of an ALP model (with an effective scale ) is considered, in which ALPs are produced in association with a gluon in a final state governed by an ALP-gluon coupling ∼ . By construction, ALP decays are suppressed and the ALP leaves the detector undetected, leading to a monojet final-state topology.
A variety of models of WIMP dark matter at the LHC involve the Higgs boson acting as a portal between the dark sector and the SM sector, either via direct Yukawa couplings to fermionic dark-matter candidates or via other mechanisms. The decay of the Higgs boson into dark-matter particles translates into a signature of miss T in the final state. Searches for invisible Higgs boson decays have been carried out at ATLAS and CMS, considering different SM Higgs production processes and different center-of-mass energies, leading to a 95% CL upper limit on the invisible Higgs boson branching ratio of 0. 26 [37] and 0.19 [38], respectively.
In this publication, a data sample corresponding to a total integrated luminosity of 139 fb −1 is used, and the analysis strategy closely follows that of the previous publication based on 36.1 fb −1 [4]. In addition, a number of improvements are implemented leading to enhanced sensitivity to new phenomena. The T requirements for identifying electrons and muons in the final state are lowered, translating into tighter lepton vetoes and a larger background reduction, which is also complemented with the inclusion of -lepton and photon vetoes. The kinematic range covered by the analysis is extended towards lower values of miss T and leading-jet T , and new control regions are defined for a better determination of backgrounds related to top-quark and -boson production processes. Finally, the analysis profits from improved theoretical predictions for +jets and +jets production, including higher-order corrections at next-to-next-to-leading order in QCD and next-to-leading order in electroweak couplings supplemented by Sudakov logarithms at two loops.
The paper is organized as follows. The ATLAS detector is described in the next Section. Section 3 provides details of the Monte Carlo simulations used in the analysis for background and signal processes. Section 4 discusses the reconstruction and identification of jets, leptons, and missing transverse momentum, while Section 5 describes the event selection. The estimation of background contributions and the study of systematic uncertainties are discussed in Sections 6 and 7. The results are presented in Section 8 and are interpreted in terms of limits in models of WIMP-pair production, ADD, SUSY in compressed scenarios, axion-like particles, new bosons in DE-inspired models, and limits on the Higgs boson invisible branching fraction. Finally, Section 9 is devoted to the conclusions.

ATLAS detector
The ATLAS detector [39] at the LHC covers nearly the entire solid angle around the collision point. 1 It consists of an inner tracking detector surrounded by a thin superconducting solenoid, electromagnetic and hadronic calorimeters, and a muon spectrometer incorporating three large superconducting toroidal magnets.
The inner-detector system is immersed in a 2 T axial magnetic field and provides charged-particle tracking in the range | | < 2.5. The high-granularity silicon pixel detector covers the vertex region and typically provides four measurements per track, the first hit normally being in the insertable B-layer installed before Run 2 [40,41]. It is followed by the silicon microstrip tracker, which usually provides eight measurements per track. These silicon detectors are complemented by the transition radiation tracker (TRT), which enables radially extended track reconstruction up to | | = 2.0. The TRT also provides electron identification information based on the fraction of hits (typically 30 in total) above a higher energy-deposit threshold corresponding to transition radiation. 1 ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the center of the detector and the -axis along the beam pipe. The -axis points from the IP to the center of the LHC ring, and the -axis points upwards. Cylindrical coordinates ( , ) are used in the transverse plane, being the azimuthal angle around the -axis. The pseudorapidity is defined in terms of the polar angle as = − ln tan( /2). Angular distance is measured in units of Δ ≡ √︁ (Δ ) 2 + (Δ ) 2 .
The calorimeter system covers the pseudorapidity range | | < 4.9. Within the region | | < 3.2, electromagnetic calorimetry is provided by barrel and endcap high-granularity lead/liquid-argon (LAr) calorimeters, with an additional thin LAr presampler covering | | < 1.8 to correct for energy loss in material upstream of the calorimeters. Hadronic calorimetry is provided by the steel/scintillator-tile calorimeter, segmented into three barrel structures within | | < 1.7, and two copper/LAr hadronic endcap calorimeters. The solid angle coverage is completed with forward copper/LAr and tungsten/LAr calorimeter modules optimized for electromagnetic and hadronic measurements respectively.
The muon spectrometer comprises separate trigger and high-precision tracking chambers measuring the deflection of muons in a magnetic field generated by the superconducting air-core toroids. The field integral of the toroids ranges between 2.0 and 6.0 T m across most of the detector. A set of precision chambers covers the region | | < 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 | | < 2.4 with resistive-plate chambers in the barrel, and thin-gap chambers in the endcap regions.
Events of interest are selected to be recorded by the first-level trigger system implemented in custom hardware, followed by selections made by algorithms implemented in software in the high-level trigger [42]. The first-level trigger accepts events from the 40 MHz bunch crossings at a rate below 100 kHz, which the high-level trigger reduces in order to record events to disk at about 1 kHz.

Monte Carlo simulation
Monte Carlo (MC) simulated event samples are used to compute detector acceptance and reconstruction efficiencies, determine signal and background contributions, and estimate systematic uncertainties in the final results. The SM background samples were processed with the full ATLAS detector simulation [43] based on G 4 [44]. Signal simulated samples, with the exception of those for Higgs production, were processed with a fast simulation using a parameterization of the calorimeter response and G 4 for the other parts of the detector. Simulated events are then reconstructed and analyzed with the same analysis chain as for the data, using the same trigger and event selection criteria. The effects of multiple proton-proton interactions in the same or neighboring bunch-crossings (pileup) were taken into account by overlaying the hard-scattering process with simulated minimum-bias events, distributed according to the frequency in data and generated by P 8.186 [45] with the A3 set of tuned parameters (tune) [46] and the NNPDF2.3LO parton distribution function (PDF) set [47]. Correction factors are applied to the Monte Carlo simulation to account for differences between simulation and the data in pileup, the energy and momentum scales, and reconstruction and identification efficiencies of physics objects.

Signal simulation
Simulated samples for the ADD LED model with different numbers of extra dimensions in the range = 2-6 and a fundamental scale in the range 3-12 TeV were generated using P 8.205 with the A14 tune [48] and NNPDF2.3LO PDFs. The cross section is computed at next-to-leading order (NLO) accuracy in the strong coupling constant. The renormalization scale was set to the geometric mean of the squared transverse masses of the two produced particles,

√︃
( 2 T, + 2 ) ( 2 T, + 2 ), where T, and ( T, and ) denote, respectively, the transverse momentum and the mass of the KK graviton (parton) in the final state. The factorization scale was set to the smaller of the transverse masses, √︃ 2 T + 2 , of the KK graviton and the parton.
SUSY signals for squark-pair production were generated with M G 5_aMC@NLO v2.2.3 [49] and interfaced to P 8.186 with the A14 tune for modeling of the squark decay, parton showering, hadronization, and the underlying event. The PDF set used for the generation was NNPDF23LO, and the renormalization and factorization scales were set to = √︃ 2 + 2 T, , where the sum runs over all final-state particles from the hard-scatter process. The matrix-element calculation was performed at tree level, and includes the emission of up to two additional partons. Matching to parton-shower calculations was accomplished by using the CKKW-L prescription [50], with a matching scale set to one quarter of the pair-produced superpartner mass. All signal cross sections were calculated to approximate next-to-next-to-leading order (NNLO) in the strong coupling constant, adding the resummation of soft gluon emission at next-to-next-to-leading-logarithm accuracy (approximate NNLO+NNLL) [51][52][53][54]. The nominal cross section and its uncertainty were taken from an envelope of cross-section predictions using different PDF sets and factorization and renormalization scales, as discussed in Ref. [55]. Simulated samples were produced with squark masses in the range between 250 GeV and 1.2 TeV, and squark-neutralino mass differences Δ varying between 5 GeV and 50 GeV.
WIMP -channel signal samples were simulated in P -B v2 [56][57][58] (revision 3049) using two implementations of simplified models, introduced in Ref. [59]. The DMV model of WIMP-pair production was used for -channel spin-1 axial-vector mediator exchange at NLO in the strong coupling constant, and the DMS_tloop model was used for WIMP-pair production with -channel spin-0 pseudoscalar mediator exchange with the full quark-loop calculation at leading order (LO) [60]. Renormalization and factorization scales were set to T /2 on an event-by-event basis, where T = √︃ 2 + 2 T, 1 + T, 1 is defined by the invariant mass of the WIMP pair ( ) and the transverse momentum of the highest-T parton-level jet ( T, 1 ). The mediator propagator is described by a Breit-Wigner distribution. Events were generated using the NNPDF30 [47] PDFs and interfaced to P 8.205 with the A14 tune [48] for parton showering, hadronization and the underlying event. Couplings of the mediator to WIMP particles and those of the SM quarks were set to = 1 and = 1/4, respectively, for the axial-vector mediator model whereas both couplings were set to one in the case of the pseudoscalar mediator model, following the conventions of the LHC DM Working Group [17,18]. Each model was simulated for a range of possible WIMP and mediator masses, with WIMP masses ranging from 1 GeV to 1 TeV and mediator masses between 10 GeV and 10 TeV.
Samples of simulated events for ALP production in association with a jet [36] were generated at leadingorder (LO) accuracy in the strong coupling constant with M G 5_aMC@NLO v2.6.2 and interfaced to P 8.240 with the A14 tune for modeling of parton showering, hadronization, and the underlying event. The PDF set used for the generation was NNPDF23LO, and the renormalization and factorization scales were set to half of the transverse mass, 0.5 × √︃ 2 T + 2 , of the ALP and the parton. Other processes related to the coupling of the ALP to photons, vector bosons or the Higgs boson are suppressed. Values for the ALP mass up to = 1 GeV and values for the coupling to gluons up to ∼ = 1 were considered. Effective scales in the range between 1 TeV and 10 TeV are explored.
Simulated events for the dark-energy model were generated using an effective field theory implementation [31] in M G 5_aMC@NLO v2.6.1 at LO accuracy in the strong coupling constant. Following the work in Ref.
[6], only terms corresponding to the L 2 operator, relevant for the monojet final-state topology, were considered, with the Wilson coefficient 2 = 1 and the rest of the Wilson coefficients ( ) set to zero. Electroweak terms were vetoed and only one insertion of a L 2 operator in each diagram was allowed. The generated events were interfaced to P 8.240 with the A14 tune for modeling of parton showering, hadronization, and the underlying event. The PDF set used for the generation was NNPDF23LO, and the renormalization and factorization scales were set to 0.5 × T = √︃ 2 + 2 T, 1 + T, 1 , where is the invariant mass of the two scalar particles in the final state. The dark-energy field mass and the coupling to gluons were set to = 100 MeV and * = 4 , respectively. Effective scales 2 up to 3 TeV are explored.
Simulated samples for the production of a 125 GeV Higgs boson were generated, with NLO accuracy in QCD emissions, using the P -B v2 [61] event generator. The samples include gluon-gluon fusion processes ( → and → ), vector-boson fusion (VBF) processes ( → ), the associated production with a / boson in the final state ( ), and the associated production with a¯pair in the final state (¯+ ). The simulated events were interfaced with P 8.212 for parton shower, hadronization and underlying-event modeling using the AZNLO tune [62] with the NNPDF30+CTEQ6L1 PDF in the case of → and → , CT10 in the case of , and NNPDF30 PDFs in the case of → and¯+ processes. The → sample was normalized such that it reproduces the total cross section predicted by a next-to-next-to-next-to-leading-order (NNNLO) QCD calculation with NLO electroweak (EW) corrections applied, and → and processes were normalized to cross sections calculated at NNLO in QCD with NLO EW corrections. The → sample was normalized to cross sections calculated at NLO in QCD, and the¯+ sample was normalized to cross sections calculated at NLO in QCD with NLO EW corrections [63]. In all cases, the Higgs boson invisible decay → * → 4 is considered because it provides final-state topologies consistent with those from models of new phenomena with invisibly decaying Higgs bosons.

Background simulation
After applying the final-state selection as described in Section 5, the primary SM background contributing to monojet event signatures is → + jets. There are also significant contributions from + jets events, primarily from → + jets, with unidentified leptons in the final state. Small contributions are expected from → ℓℓ + jets (ℓ = , , ), multĳet,¯, single-top, and diboson ( , , ) processes. Contributions from top-quark production associated with additional vector bosons (¯+ ,¯+ , or + + / processes) are negligible and not considered in this analysis. As discussed in detail in Section 6, the contribution from SM background processes in the signal regions are determined using simulated samples constrained with data in control regions. In the following, the generation of the different simulation samples is described.
Events containing or bosons with associated jets were simulated using the S 2.2.1 [64] event generator. Matrix elements (ME) were calculated for up to two partons at NLO and four partons at LO using OpenLoops [65] and Comix [66], and merged with the S parton shower (PS) [67] using the ME+PS@NLO prescription [68]. The NNPDF3.0NNLO [47] PDF set was used in conjunction with a dedicated parton-shower tuning developed by the authors of S . The MC predictions were initially normalized to NNLO perturbative QCD (pQCD) predictions according to DYNNLO [69,70] using the MSTW2008 90% CL NNLO PDF set [71].
In order to improve the description of +jets and +jets processes, their MC predictions were reweighted to account for higher-order QCD and electroweak corrections. The reweighting procedure is based on partonlevel predictions for / +jets production from Ref. [72], which include NNLO QCD corrections [73][74][75][76] and NLO electroweak corrections [77][78][79][80] supplemented by Sudakov logarithms at two loops [81][82][83][84]. These corrections are provided separately for +jets, → ℓ + ℓ − +jets and → +jets processes, as a function of the vector-boson T , in order to improve the description of the measured -boson T distribution [85]. The reweighting procedure takes into account the difference between the QCD NLO predictions as included already in S and as provided by the parton-level calculations. Uncertainties in these higher-order corrections and their correlations across processes are described in Section 7.
Separate nonoverlapping samples for / +jets production via VBF-driven processes were generated using Herwig++ (v7.1.3 for electron and -lepton decays and v7.2 for muon decays) [86]. The samples were produced at NLO accuracy in pQCD using VBFNLO v3.0.0 [87]. The NNPDF30 PDF set was used along with the default set of tuned parameters for parton showering, hadronization and the underlying event. The EvtGen v1.2.0 program [88] was used to model the decays of the bottom and charm hadrons.
For the generation of¯and single-top-quark events in the -channel and -channel, the P -B v2 [61] event generator was used with CT10 [89] PDFs. Electroweak -channel single-top-quark events were generated using the P -B v1 event generator. This event generator uses the four-flavor scheme to calculate NLO matrix elements, with the CT10 four-flavor PDF set. Interference occurring beyond tree level between and¯processes was studied, considering both the diagram subtraction (DS) and diagram removal (DR) production schemes [90]; DR was used for the nominal background prediction, DS for the evaluation of systematic uncertainties as described in Section 7. The samples were normalized to NNLO pQCD predictions. The parton shower, hadronization, and underlying event were simulated using P 8.205 with the A14 tune. The top-quark mass was set to 172.5 GeV. The EvtGen v1.2.0 program was used to model the decays of the bottom and charm hadrons. Alternative samples were generated using M G 5_aMC@NLO (v2.2.1) and P -B interfaced to Herwig++ (v7.1.3) [86] in order to estimate the effects of the choice of matrix-element event generator and parton-shower algorithms, and fragmentation and hadronization effects. The EvtGen v1.2.0 program was used to model the decays of the bottom and charm hadrons.
Diboson samples ( , , and production) were generated using S 2.2.1 or S 2.2.2 with NNPDF3.0NNLO, and were normalized to NLO pQCD predictions [91]. The EvtGen v1.2.0 program was used to model the decays of the bottom and charm hadrons.

Event reconstruction
Jets are reconstructed from energy deposits in the calorimeters[92] using the anti-jet algorithm [93] as provided by the [94] toolkit, with the radius parameter = 0.4. The measured jet four-momentum is calibrated using information from both simulation and data [95]. In addition, jets are corrected for contributions from pileup. Jets with T > 20 GeV and | | < 2.8 are considered in the analysis. A combination of track-based variables developed to suppress pileup jets, called the jet-vertex tagger (JVT) [96], is constructed. In order to remove jets originating from pileup collisions, for central jets (| | < 2.5) with T < 120 GeV a significant fraction of the tracks associated with each jet must have an origin compatible with the primary vertex, as defined by the jet-vertex tagger.
Jets with T > 30 GeV and | | < 2.5 are identified as jets containing -hadrons ( -jets) if tagged by a multivariate algorithm which uses information about the impact parameters of inner-detector tracks matched to the jet, the presence of displaced secondary vertices, and the reconstructed flight paths of -and -hadrons inside the jet [97,98]. A 60% efficient -tagging working point, as determined in a simulated sample of¯events, is chosen. This corresponds to rejection factors of approximately 1500, 35 and 180 for light-quark and gluon jets, -jets, and -leptons decaying hadronically, respectively.
Electrons are found by combining energy deposits in the calorimeter with tracks found in the inner detector. They are initially required to have T > 7 GeV and | | < 2.47, and to satisfy the 'Loose' electron shower shape and track selection criteria described in Ref. [99], including a requirement on the match between the track and the primary vertex, which requires the longitudinal impact parameter | 0 | sin to be less than 0.5 mm. Overlaps between identified electrons and jets with T > 30 GeV in the final state are resolved. Jets are discarded if they are not -tagged and their separation Δ = √︁ (Δ ) 2 + (Δ ) 2 from an identified electron is less than 0.2. Otherwise, the electron is removed as it most likely originates from a semileptonic -hadron decay. The electrons separated by Δ between 0.2 and 0.4 from any remaining jet are removed.
Muon candidates are formed by combining information from the muon spectrometer and inner tracking detectors. They are required to pass 'Medium' identification requirements [100], and to have T > 7 GeV and | | < 2.5. As in the case of electrons, the muon track is required to have | 0 | sin < 0.5 mm. Jets with T > 30 GeV and fewer than three tracks with T > 500 MeV associated with them are discarded if their separation Δ from an identified muon is less than 0.4. The muon is discarded if it is matched to a jet with T > 30 GeV that has at least three tracks associated with it. If an electron and a muon share the same inner-detector track, the muon is retained and the electron is discarded in order to remove electron candidates originating from muon bremsstrahlung followed by photon conversion.
Hadronically decaying -lepton candidates are formed by combining information from the calorimeters and inner tracking detectors. The -lepton reconstruction algorithm [101] is seeded by reconstructed jets with T > 10 GeV and | | < 2.5, and the reconstructed energies of the -lepton candidates are corrected to the -lepton energy scale [102]. They are required to pass 'Loose' identification requirements [103], to have T > 20 GeV and | | < 2.5, excluding the transition region between the electromagnetic barrel and endcap calorimeters (1.37 < | | < 1.52), and to have one or three associated charged tracks. The -leptons close to electrons or muons (Δ < 0.2) are removed. Any jet within Δ = 0.2 of a -lepton is removed.
Photons are reconstructed from clusters of energy deposited in the electromagnetic calorimeter. They are required to pass 'Tight' identification requirements [99], and to have T > 10 GeV and | | < 2.37. Photons are discarded if their separation Δ from an identified muon or electron is less than 0.4. Jets are instead discarded if their separation Δ from an identified photon is less than 0.4.
The vector missing transverse momentum p miss T is reconstructed from the negative vectorial sum of the transverse momenta of electrons, muons, -leptons, photons, and jets with T > 20 GeV and | | < 4.5. Tracks compatible with the primary vertex but not associated with any of those objects are also included in the vectorial sum, as described in Section 3.4.2 of Ref. [104].

Event selection
This analysis is based on data collected by ATLAS during Run 2 of the LHC, corresponding to a total integrated luminosity of 139 fb −1 . The data were collected using a trigger based on a requirement on miss T as computed from calorimetry information at the final stage of the two-level trigger system [105]. After analysis selections, the trigger was measured to be fully efficient for events with miss T > 200 GeV, as determined using a data sample with muons in the final state.
Events are required to have at least one reconstructed primary vertex consistent with the beamspot envelope and containing at least two associated tracks of T > 500 MeV. When more than one such vertex is found, the vertex with the largest summed 2 T of the associated tracks is chosen. Events having identified muons, electrons, photons or -leptons in the final state are vetoed. Selected events have miss T > 200 GeV, a leading jet with T > 150 GeV and | | < 2.4, and up to three additional jets with T > 30 GeV and | | < 2.8. Separation in the azimuthal angle of Δ (jet, p miss T ) > 0.4 (0.6) between the missing transverse momentum direction and each selected jet is required for events with miss T > 250 GeV (200 GeV < miss T ≤ 250 GeV) to reduce the multĳet background contribution, since large miss T can originate from jet energy mismeasurement. Jet quality criteria [106] are imposed, which involve selections based on quantities such as the pulse shape of the energy depositions measured in the cells of the calorimeters, electromagnetic energy fraction in the calorimeter, maximum fraction of the jet energy collected by a single calorimeter layer, and the charged-particle fraction. 2 Loose selection criteria are applied to all jets with T > 30 GeV and | | < 2.8, which remove anomalous energy depositions due to coherent noise and electronic noise bursts in the calorimeter [107]. Events with any jet not satisfying the loose criteria [106] are discarded. Noncollision backgrounds, for example energy depositions in the calorimeters due to muons of beaminduced or cosmic-ray origin, are suppressed by imposing tight selection criteria on the leading jet: the ratio of the jet charged-particle fraction to the maximum fraction of the jet energy collected by a single calorimeter layer, ch / max , is required to be larger than 0.1. Jet quality requirements altogether have a negligible effect on the signal efficiency.
The signal region (SR) is divided into different bins of miss T , which are listed in Table 1. Inclusive bins are used for a model-independent interpretation of search results, while the full set of exclusive bins are used for the interpretation within different models of new physics.

Background estimation
A semi-data-driven technique, supported by statistically independent control regions, is used to constrain the normalization of Standard Model backgrounds. The approach followed is similar to the one used in previous versions of the analysis [4].

Control regions
The estimation of the + jets, + jets,¯, and single-backgrounds is performed using five control regions, as described below. These regions are defined in a way similar to the SR: events are selected in terms of a quantity which is -similarly to p miss T in the SR -a proxy for the transverse momentum of the system which recoils against the hadronic activity in the event. This quantity is denoted in the following by p recoil T , and its magnitude by recoil T . The same selection criteria for jet multiplicity and leading jet T as in the SR are applied in the control regions, with the same requirements on the azimuthal separation of jets from p recoil T .
Control regions are binned in terms of recoil T , using the same binning as in the signal region (see Table 1). In the signal region, recoil T is equivalent to miss T . A control region enriched in → events is defined by selecting events that pass the same trigger requirements as in the signal region, if they have exactly one reconstructed muon and this muon has T > 10 GeV and passes the requirement on the transverse impact parameter significance, 0 / ( 0 ), to be less than 3, and if no electrons, -leptons, photons or -jets are reconstructed. In this region, recoil T is defined as the magnitude of the vector sum of the missing transverse momentum and the muon transverse momentum, |p miss T + p T ( )|, and is required to be higher than 200 GeV. An additional requirement on the transverse mass is applied, 30 ] and the neutrino transverse momentum, p T ( ), is taken to be the same as p miss T . Similarly, a control region enriched in → events is defined by selecting events that pass the same trigger requirements but have exactly two reconstructed muons, where these muons have T > 10 GeV and 0 / ( 0 ) < 3, and the invariant mass of the dimuon system is between 66 and 116 GeV. In this region, recoil T is defined as the magnitude of the vector sum of the missing transverse momentum and the transverse momentum of the dimuon system, |p miss T + p T ( )|, and is required to be higher than 200 GeV. The trigger requirements used for these two regions do not include muon information in the calculation of miss T , and are fully efficient for events satisfying the selection criteria.
A control region enriched in → events is defined by selecting events that pass single-electron triggers, if they have exactly one reconstructed electron and this electron satisfies tight identification criteria described in Ref.
[103], is reconstructed outside the transition region between the electromagnetic barrel and endcap calorimeters, has T > 30 GeV and 0 / ( 0 ) < 5, and passes the tight isolation requirements based on information from the electromagnetic calorimeter and from tracking detectors, described in Ref. [99]. In this region, recoil T is defined as the magnitude of the vector sum of the missing transverse momentum and the electron transverse momentum, |p miss T + p T ( )|, and is required to be higher than 200 GeV. The transverse mass is required to be 30 GeV < T < 100 GeV. In order to further suppress backgrounds from multĳet processes with jets misidentified as high-T electrons, the events are required to have miss T > 70 GeV and miss T / √ T > 5 GeV 1/2 , where T denotes the scalar sum of the T of the identified jets in the final state.
Similarly, a control region enriched in → events is defined by selecting events with exactly two reconstructed electrons, where these electrons have T > 30 GeV and 0 / ( 0 ) < 5, and the invariant mass of the dielectron system is between 66 and 116 GeV. In this region, recoil T is defined as the magnitude of the vector sum of the missing transverse momentum and the transverse momentum of the dielectron system, |p miss T + p T ( )|, and is required to be higher than 200 GeV. The single-electron trigger requirements are fully efficient for events satisfying the selection criteria for these two regions.
A control region enriched in¯and single-events is defined by selecting events which pass the same cuts as for the → and → regions, but which have at least one identified -jet.   Table 2 shows a summary of the selection criteria for all regions.

Multĳet background
The multĳet background with large miss T originates mainly from the misreconstruction of the energy of a jet in the calorimeter and, to a lesser extent, is due to the presence of neutrinos in the final state from heavy-flavor hadron decays. In this analysis, the multĳet background is determined from data, using the jet smearing method as described in Ref. [108]. It relies on the assumption that the miss T value of multĳet events is dominated by fluctuations in the jet response in the detector, which can be measured in the data. The method was checked using a validation region where events were selected as in the signal region, except for a modified requirement that the minimum azimuthal distance between a jet and p miss T is between 0.3 and 0.4. After event selection, the multĳet background is estimated to be about 1.2%, 0.8%, 0.4% and 0.3% of the total background in the exclusive signal region bins EM0, EM1, EM2 and EM3, respectively, and it is less than 0.1% for the other signal region bins. A conservative 100% uncertainty is assigned to the normalization of this background.

Noncollision background
After event selections are applied, the signal region may contain residual contributions from noncollision backgrounds. These backgrounds, which are not included in simulation, mainly arise when beam-halo protons intercept the LHC collimators, leading to particle cascades which produce muons. The remaining contributions are estimated following the methods set out in Ref. [107]. In particular, the jet timing, , calculated from the energy-weighted average of the time of the jet energy deposits, defined relative to the event time in nominal collisions, is used. A dedicated region enhanced in beam-induced background, defined by inverting the tight jet-quality selection imposed on the leading jet, is used to estimate the amount of non-collision background from the fraction of events with a leading-jet timing | | > 5 ns. The results indicate a contribution at the per-mille level from noncollision backgrounds in the signal region. A conservative 100% uncertainty is assigned to the normalization of this background.

Standard Model background fit
The estimation of backgrounds in the SR is based on a simultaneous, binned likelihood fit to the recoil T distribution of the five control regions described in Section 6.1. The number of events in each region and in each bin is treated as a random variable with a Poisson distribution function, with an expectation value given by the sum of the SM predictions for each background in that bin. The likelihood fit is based on the profile likelihood method [109]. Systematic uncertainties are represented by Gaussian-distributed nuisance parameters, and take into account the correlation among systematic variations and across recoil T bins.
The normalization of all + jets and + jets processes, excluding those initiated by VBF, is multiplied by a common single floating normalization factor, which is the same across all recoil T bins. As a result, data from both and control regions are used simultaneously to constrain the → background in the signal region. Systematic uncertainties in + jets and + jets event yields, as described in Section 7, cover the residual bin-by-bin differences among processes when higher-order calculations are included, taking into account the correlation of theoretical uncertainties across different processes with the calculation provided in Ref. [72]. Similarly, one floating normalization factor is used for each of the¯and singlebackgrounds, resulting in a total of three floating background normalization factors in the fit. Compared to the previous version of the analysis, the usage of two independent normalization factors for the two main sources of top-quark backgrounds is introduced to better take into account their different expected contribution as a function of recoil T . Table 3 shows the results of the background-only fit to the control regions, when all exclusive bins are fitted simultaneously. As determined in the signal region, the normalizations of the + jets and + jets backgrounds get corrected by a multiplicative factor of 1.13 ± 0.01, while the normalization of the¯and single-backgrounds gets corrected by a multiplicative factor of 0.9 ± 0.1 and 1.6 ± 0.4, respectively. in the control regions. The shown expected distributions include the data-driven normalization factors as extracted from the binned likelihood fit to the different exclusive recoil T bins in the control regions. Good agreement is observed, within statistical and systematic uncertainties, with data. As an illustration, 2 -statistical tests, using the binned profile likelihood fit described above, probing potential shape discrepancies between the observed Table 3: Data and expected events with recoil T > 200 GeV in the five control regions (top: post-fit, bottom: pre-fit). The post-fit predictions for the SM backgrounds are obtained after the simultaneous binned likelihood fit to the five control regions, performed in the exclusive bins of recoil T (EM0-EM12). The background predictions include both the statistical and systematic uncertainties. The individual uncertainties are correlated, and do not necessarily add in quadrature to equal the total background uncertainty. The dash "-" denotes contributions of less than 0.01% to the total background. In order to perform model-independent tests for new physics processes, discussed in Section 8.1, the same fit procedure is repeated in each of the inclusive bins of recoil T for signal and control regions, denoted in Table 1 by IM0-IM12. Since in this case no shape information is available to constrain the separate contributions of¯and single-, a single normalization factor is used for all top-quark-related processes, along with the normalization factor for / +jets, resulting in two free background normalization factors in the fit. Additionally, the nuisance parameters related to systematic uncertainties refer to the given miss T inclusive region. A total of 13 separate fits are therefore performed, based on five control regions each and including two free background normalization factors. The results are expected to differ from those of the simultaneous fit to exclusive bins, due to the lack of recoil T shape information to constrain uncertainties and

Systematic uncertainties
The impact of systematic uncertainties is estimated after performing a background-only fit to data from the exclusive CRs, and evaluating the impact of the uncertainty in the total background yield in each bin of recoil T in the SR. The dominant sources of experimental uncertainty are those related to the electron, muon and jet identification and reconstruction efficiencies, while uncertainties in the + jets predictions give the leading contribution to theory uncertainties. More details are provided in the following sections.

Background uncertainties
The uncertainty in the combined 2015-2018 integrated luminosity is 1.7%. It is derived from the calibration of the luminosity scale using -beam-separation scans, following a methodology similar to that described in Ref. [110], and using the LUCID-2 detector for the baseline luminosity measurements [111]. This uncertainty nearly cancels out in the semi-data-driven background estimation procedure, and translates into a residual uncertainty in the total background in the SR of less than 0.01% (0.05%) for recoil Uncertainties in the electron reconstruction and identification efficiencies are computed following the method described in Ref. [99]; the latter are treated as uncorrelated between selected and vetoed electrons, since different working points are used for their identification, as described in Section 5. Uncertainties in the electron and photon energy scale and resolution are computed following the method described in Ref. [114]. Overall, they translate into uncertainties in the total background in the SR between 0.7% and 1.3% for recoil T between 200 GeV and 1200 GeV. Uncertainties due to the electron isolation efficiency give a contribution of less than 0.2% across the recoil T spectrum. Negligible contributions are given by the electron trigger efficiency and by the photon identification efficiency. Uncertainties in the muon reconstruction and identification efficiencies and in their momentum measurement are computed following the method described in Ref. [100]. In order to take into account the difference between the simulated and measured identification efficiencies for muons with T above 300 GeV, an additional uncertainty is included, conservatively taken as uncorrelated in muon T and . Overall, these translate into uncertainties in the total background in the SR between 0.4% and 1.9% for recoil T between 200 GeV and 1200 GeV. Uncertainties in the -lepton reconstruction and identification efficiencies translate into uncertainties in the total background in the SR of 0.1% (0.07%) for recoil T = 200 GeV (> 1200 GeV).
Uncertainties in the higher-order QCD and electroweak parton-level calculations used to correct the MC prediction for + jets processes not initiated by VBF are calculated following the procedure described in Ref. [72]. They are provided in the form of event weights parameterized as a function of vector-boson T , which are applied to derive shape and normalization uncertainties for simulated + jets processes in signal and control regions. The correlations across recoil T bins are implemented as recommended in Ref. [72]. The correlations across processes are implemented as follows.
Three sources of pure QCD uncertainties are considered. The uncertainty associated with the truncation of the perturbative expansion in the strong coupling constant is estimated by varying the QCD renormalization and factorization scales both individually and simultaneously by factors 2 and 0.5, and evaluating the change in differential cross section in bins of the vector-boson T for these seven combinations. The center of the resulting band is taken as the nominal estimate, and its half width is taken as its systematic uncertainty. Uncertainties in the shape of the vector-boson T distribution, which are relevant for the extrapolation of low-T measurements to high T , are taken into account by applying an additional uncertainty estimated from a conservative shape distortion of the aforementioned scale uncertainty. 3 These two uncertainties are represented by two nuisance parameters, (1) NNLO and (2) NNLO , which are taken as correlated across + jets processes, assuming that for recoil T , the QCD effects on the + jets and + jets predictions are very similar. Residual differences in QCD corrections between + jets and + jets processes are estimated from the difference in QCD NNLO -factors with respect to + jets production, and taken into account as an additional nuisance parameter, (3) NNLO .
Three sources of pure EW uncertainties and one source of mixed QCD-EW uncertainties are considered. Unknown Sudakov logarithms beyond NNLO are considered as the dominant source of uncertainty at high T , and are treated as correlated across + jets processes and represented by one nuisance parameter, (1) nNLO EW . An additional source of uncertainty is considered to cover possible NNLO effects not included in the calculation, conservatively defined as 5% of the absolute full NLO EW correction, and is treated as uncorrelated across + jets processes and hence represented by the three nuisance parameters (2) ( ) nNLO EW , (2) ( →ℓ + ℓ − ) nNLO EW , and (2) ( → ) nNLO EW . The uncertainty in the limitations of the Sudakov approximation at two loops is estimated as the difference between the NLL Sudakov approximation and the exponentiation of the full NLO EW correction, and is treated as uncorrelated between + jets and + jets processes, resulting in two nuisance parameters, (3) ( ) nNLO EW and (3) ( ) nNLO EW . Uncertainties due to the approximation of mixed QCD-EW corrections via a factorized combination of QCD and EW corrections are assumed to be proportional to the difference between the additive and multiplicative combination of QCD and EW corrections, and are treated as correlated across + jets processes, resulting in a single nuisance parameter, NNLO mix .

Different definition of -leptons between parton-level calculation and simulation
Correlated across recoil T bins and + jets processes -Uncertainties in the parton distribution functions are treated as correlated across +jets processes, following the prescription of Ref. [72]. They are estimated by the sum in quadrature over the 107 independent Hessian PDF replicas provided by the PDF set LUXqed_plus_PDF4LHC15_nnlo, following Eq. (20) of Ref. [115]. The resulting nuisance parameter is denoted by PDF . Table 4 summarizes the considered nuisance parameters and their assumed correlations. Before the CR-only fit, the leading impacts on the signal region background prediction for the EM0 selection come from (1) NNLO (1.8%), (2) NNLO (1.5%) and PDF (0.7%), while the largest contributions for the EM12 selection come from PDF (2.9%), (1) NNLO (2.8%), (3) ( ) nNLO EW (1.6%) and (2) NNLO (1.5%). After the CR-only fit, these uncertainties translate into uncertainties in the total background in the SR between 0.4% and 2% for recoil ). An additional systematic uncertainty is included to cover possible differences between the definition of -leptons at Monte Carlo generator level and the one used in the theoretical calculation from Ref. [72], which translates into uncertainties in the total background in the SR between 0.05% and 0.1% for recoil T between 200 GeV and 1200 GeV.
Uncertainties in the + jets processes initiated by VBF include scale and PDF uncertainties and the comparison with S as an alternative MC generator. They translate into uncertainties in the total  Uncertainties in the theoretical predictions of the¯and single-backgrounds are estimated for the two processes separately by varying parton-shower parameters and the amount of initial-and final-state soft gluon radiation, by comparing predictions from different MC event generators [116] and by comparing the degree of interference between single-in the -channel and¯when using the DR and DS schemes described in Ref. [117]. In the case of¯(single-), they translate into uncertainties in the total background in the SR between 0.06% (0.13%) and 0.7% (0.28%) for recoil T between 200 GeV and 1200 GeV.
Uncertainties in the theoretical predictions of diboson backgrounds include uncertainties in the QCD renormalization, factorization and resummation scales, uncertainties due to the choice of parton distribution functions and uncertainties in the modeling of the parton showers. They translate into uncertainties in the total background in the SR between 0.01% and 0.22% for recoil T between 200 GeV and 1200 GeV.
Uncertainties in the multĳet and noncollision backgrounds translate into uncertainties in the total background in the SR for recoil T = 200 GeV of 1% and 0.2%, respectively, and are negligible above 800 GeV. Table 5 summarizes the overall impact of systematic uncertainties in each bin of recoil T in the SR, as estimated from the CR-only fit.

Signal uncertainties
Sources of systematic uncertainty in the predicted signal yields are considered separately for each model of new physics, using a common set of procedures. Experimental uncertainties include those related to the jet and miss T reconstruction, energy scales and resolutions, which introduce uncertainties in the signal yields for the different models that vary in the range between 1% and 3% at low recoil T , and between 4% and 7% at large recoil T , depending on the parameters of the model. The 1.7% uncertainty in the integrated luminosity is also included. Other uncertainties related to the jet quality requirements are negligible.
Uncertainties affecting the signal acceptance in the generation of signal samples include: uncertainties in the modeling of the initial-and final-state radiation and the underlying event, determined using simulated samples with modified parton-shower parameters (by factors of two or one half); uncertainties due to PDFs and variations of the s ( ) value employed, as computed from the envelope of CT10 or CT14, MMHT2014 [118] and NNPDF30 error sets; and uncertainties due to the choice of renormalization and factorization scales, which are varied by factors of two or one half. In addition, theoretical uncertainties in the predicted cross sections, including PDF and renormalization-and factorization-scale uncertainties, are assessed and their effect is shown in terms of variations of the observed results.
In the case of WIMP production models, the uncertainty related to the modeling of the initial-and final-state radiation translates into a 3% to 6% uncertainty in the signal acceptance. The choice of different PDF sets results in up to a 10% and a 20% uncertainty in the case of axial-vector and pseudoscalar models, respectively. Varying the renormalization and factorization scales introduces 0.1% to 21% variations in the signal acceptance, depending on the model and the mediator and WIMP masses considered. Renormalization and factorization scale uncertainties introduce an uncertainty in the cross-section predictions of about 10% in the case of the axial-vector mediator model and up to 50% for the pseudoscalar mediator model. Finally, PDF uncertainties translate into cross-section uncertainties of about 5% and 20% for the axial-vector and pseudoscalar mediator models, respectively.
Similarly, for SUSY models, the uncertainties related to the modeling of initial-and final-state gluon radiation and the matching between matrix elements and parton showers in the simulation translate into a 7% to 8% uncertainty in the signal acceptance. Variations of the renormalization and factorization scales introduce an uncertainty of about 3% in the signal acceptance. Uncertainties in the predicted cross sections, including both renormalization/factorization scale and PDF uncertainties, increase with the squark masses and range between 7% for a mass of 100 GeV and about 11% for a mass of about 1 TeV.
In the case of dark-energy-inspired models, uncertainties related to renormalization/factorization scales, PDFs, and parton-shower modeling vary the signal acceptance by 0.1% to 3.5%, 1% to 16%, and 0.1% to 5%, respectively, with increasing miss T . Renormalization/factorization scale and PDF uncertainties introduce variations in the cross-section predictions of about 30% each. For the ADD model, the uncertainties related to the modeling of the initial-and final-state gluon radiation translate into uncertainties in the ADD signal acceptance which vary between 11% and 13% with increasing miss T and are approximately independent of . The uncertainties due to the PDFs, affecting both signal normalization and acceptance, increase from 11% at = 2 to 43% at = 6. Similarly, the variations of the renormalization and factorization scales introduce a signal yield uncertainty of 23% to 36%, growing with increasing .
For the ALPs production model, theoretical uncertainties related to PDFs, affecting signal normalization and acceptance, translate into uncertainties in the signal yields that vary in the range between 2% and 14%. Variations of the renormalization and factorization scales and matrix-elements to parton-shower matching scales, introduce uncertainties in the signal yields that vary between 5% and 50%. Variations in the parton-shower modeling translate into uncertainties in the signal acceptance in the range between 1% and 20%, depending on the miss T bin considered.
Finally, for the interpretation of an invisibly decaying Higgs boson, uncertainties related to PDFs, affecting both signal normalization and signal acceptance, translate into 0.4% to 0.8% variations in the Higgs signal yields as miss T increases. Variations in the renormalization and factorization scales introduce a 10% uncertainty in the signal yields. Uncertainties in the parton-shower modeling translate into uncertainties in the signal acceptance that vary between 3% and 9% with increasing miss T . Uncertainties in the higher-order electroweak corrections, especially relevant for VBF and processes, translate into uncertainties in the signal yield that vary between 1.4% and 10% with increasing miss T . Figure 4 shows several measured distributions in the signal region compared with the SM predictions obtained from the fit to CRs. As discussed in Section 6, the SM predictions are normalized with normalization factors determined from the global fit carried out in exclusive recoil T bins. The fitting procedure also constrains the background uncertainties, resulting in a precise SM prediction in almost the whole recoil T spectrum. As an example, the SM predictions are determined with a total uncertainty of 1.5%, 1.2%, and 4.1% for the EM0, EM4, and EM12 signal regions, respectively, which include correlations between uncertainties in the individual background contributions. For illustration purposes, the ratios of data to SM predictions are shown in the lower panel, both after the CR fit and after a global background-only fit when the signal region is also included ("SR+CR fit").

Results and interpretations
The number of events in the data and the individual background predictions are presented in Tables 6 and 7 for inclusive and exclusive recoil T bins, respectively. The results for all the signal regions are summarized in Table 8. Overall, good agreement between data and SM predictions is observed. The compatibility of the data with a SM background hypothesis is tested using the binned profile likelihood fit described above.  separately for each of the inclusive regions IM0-IM12. The results are collected in Table 9. Values of × × above 736 fb (for IM0) and above 0.3 fb (for IM12) are excluded at 95% CL.

Model-dependent exclusion limits
A simultaneous fit to the signal and control regions in the exclusive recoil T bins is performed, and used to set observed and expected 95% CL exclusion limits on the parameters of the different models under consideration. Uncertainties in the signal and background predictions, and in the luminosity are considered, and correlations between experimental systematic uncertainties in signal and background predictions are taken into account. The contamination of the control regions by signal events is negligible.

Weakly interacting massive particles
As discussed in Section 1, simplified models are considered with the exchange of an axial-vector or a pseudoscalar mediator in the -channel. In the case of the exchange of an axial-vector mediator, and for WIMP-pair production with > 2 , typical × values for the signal models with a 2 TeV mediator Table 6: Data and SM background predictions in the signal region for several inclusive recoil T selections, as determined using separate one-bin likelihood fits in the control regions. For the SM prediction, both the statistical and systematic uncertainties are included. In each signal region, the individual uncertainties for the different background processes can be correlated, and do not necessarily add in quadrature to equal the total background uncertainty. The dash "-" denotes negligible background contributions. For illustration, the expected event yields for particular signals for new phenomena are provided; in this case, the quoted errors include experimental uncertainties and theory uncertainties on the signal acceptance, as described in Sec. 7.2.   Table 7: Data and SM background predictions in the signal region for several exclusive recoil T selections, as determined using a binned likelihood fit in the control regions. For the SM prediction, both the statistical and systematic uncertainties are included. In each signal region, the individual uncertainties for the different background processes can be correlated, and do not necessarily add in quadrature to equal the total background uncertainty. The dash "-" denotes negligible background contributions. For illustration, the expected event yields for particular signals for new phenomena are provided; in this case, the quoted errors include experimental uncertainties and theory uncertainties on the signal acceptance, as described in Sec. 7.2.   an initial simulated sample generated with a minimum transverse momentum of 150 GeV. Similarly, values for × in the range between 13% and less than 1% are computed for the pseudoscalar mediator model with = 350 GeV and = 1 GeV, where 1% is already reached for the EM5 selection due to the softer recoil T spectrum. Figure 5(a) shows the observed and expected 95% CL exclusion contours in the -parameter plane for a simplified model with an axial-vector mediator, Dirac WIMPs, and couplings = 1/4 and = 1. In the region > 2 × , mediator masses up to about 2.1 TeV are excluded for = 1 GeV, extending significantly beyond previous bounds. The masses corresponding to the relic density [120] as determined by the Planck and WMAP satellites [15,16], within the WIMP dark-matter model and in the absence of any interaction other than the one considered, are indicated in this figure as a line that crosses the excluded region at ∼ 1500 GeV and ∼ 585 GeV. the ±1 theory uncertainties in the observed limit and the ±1 and ±2 ranges of the expected limit in the absence of a signal. The red curves correspond to the set of points for which the expected relic density is consistent with the WMAP measurements (i.e. Ωℎ 2 = 0.12), as computed with M DM [121]. The area on the hashed side of the red contour (e.g. to the right of the red contour in the region > 2 ) corresponds to predicted values of the relic density abundance inconsistent with the WMAP measurements. The region excluded due to perturbativity, defined by > √︁ /2 , is indicated by the gray hatched area. The dotted lines indicate the kinematic limit for on-shell production , = 2 × . In the case of the pseudoscalar mediator model, the shape of the 2 band at ∼ 350 GeV is related to the rapid increase of the signal cross section at the threshold at which the mediator mass equals twice the mass of the top quark. In the case of the axial-vector mediator model, the results are compared with previous results from the ATLAS Collaboration at √ = 13 TeV using 36.1 fb −1 [4].

Exclusive Signal Region
Similarly, Figure 5(b) presents observed and expected 95% CL exclusion contours in the -parameter plane for a simplified model with a pseudoscalar mediator, Dirac WIMPs, and couplings = 1 and = 1. For the first time, the monojet final state in the ATLAS experiment has enough sensitivity to exclude a part of the parameter space in such a model. Mediator masses below 376 GeV are excluded for very light WIMP candidates.
In the case of the axial-vector mediator model, the results are translated into 90% CL exclusion limits on the spin-dependent WIMP-nucleon scattering cross section SD as a function of the WIMP mass, following the prescriptions from Refs. [19,120]. Figure 6 shows exclusion limits for WIMP-proton and WIMP-neutron scattering cross sections as a function of the WIMP mass, compared with the results from the PICO [122] experiment, and from the LUX [123] and XENON1T [124] experiments, respectively. Stringent limits on the scattering cross section of the order of 1.4 × 10 −43 cm 2 for WIMP masses of about 100 GeV, and 3 × 10 −44 cm 2 for WIMP masses below 10 GeV are inferred from this analysis, which complement the results from direct-detection experiments.

Squark-pair production
As in previous publications, different models of squark-pair production are considered: stop-pair production with˜1 → +˜0 1 , stop-pair production with˜1 → + +˜0 1 , sbottom-pair production with˜1 → +˜0 1 , and squark-pair production with˜→ +˜0 1 ( = , , , ). In each case separately, the results are translated into exclusion limits as a function of the squark mass for different neutralino masses. The region with stop-neutralino or sbottom-neutralino mass differences below 5 GeV is not considered in the exclusion since in this regime the squarks could become long-lived. In such a compressed scenario, and for stop sbottom masses of about 600 GeV, the typical value of × for the selection criteria varies between 11% for EM0 and less than 1% for EM12, as computed using a sample with a minimum missing transverse momentum of 150 GeV. Comparable values for × are obtained in the rest of the squark-neutralino mass plane. limits as a function of the sbottom and neutralino masses for the˜1 → +˜0 1 (B = 100%) decay channel. In the scenario with˜1 −˜0 1 ∼ , this analysis extends the 95% CL exclusion limits up to a sbottom mass of 545 GeV. Finally, Figure 8(b) presents the observed and expected 95% CL exclusion limits as a function of the squark mass and the squark-neutralino mass difference for˜→ +˜0 1 ( = , , , ). In the compressed scenario, squark masses below 925 GeV are excluded at 95% CL. Altogether, these results significantly improve upon the previous exclusion limits based on 36.1 fb −1 of total integrated luminosity [4]. In the very compressed scenario, the observed limits on the squark masses are extended by more than 100 GeV.

Dark-energy-inspired model
Exclusion limits are computed for the Horndeski dark-energy model (see Section 1) with = 0.1 GeV, and considering only the terms relevant for the monojet final state, following the work described in Ref.
[6]. The sensitivity remains independent of the value considered for light particles up to masses of the order of 1 GeV. The typical value of × for the selection criteria varies between 8.2% for EM0 and less than 1% for EM12. Figure 9 shows the observed and expected contours at 95% CL on the -2 plane. Values for 2 below 1486 GeV are excluded, which represents a significant improvement over the limits previously obtained. The validity of the effective implementation of the model at the LHC energies was studied previously [6] by truncating the signal contributions with √ˆ< * 2 , where √ˆi s the center-of-mass energy of the hard interaction, leading to a negligible effect on the obtained exclusion limits.

Large extra spatial dimensions
The results are translated into limits on the parameters of the ADD model. As in previous analyses, only the signal regions with recoil T > 400 GeV are employed, with sufficient sensitivity to ADD signal. The typical value of × for the selection criteria, as computed from a simulated sample with missing transverse momentum above 150 GeV, is of the order of 6% for EM4 and is less than 1% for EM12. Figure 10 and Table 10 present the results. Values of below 11.2 TeV at = 2 and below 5.9 TeV at = 6 are excluded at 95% CL, which improve on the exclusion limits from previous results using 36.1 fb −1 of 13 TeV data [4]. As already noted in Ref. [4], the analysis partially probes the phase-space region withˆ> 2 . The suppression of this kinematic region in computing the 95% CL lower limits on translates into a negligible effect on the results.

Axion-like particles
Results are expressed in terms of 95% CL limits on the parameters of the ALP model. As in the case of the ADD model, the kinematic region with recoil T > 400 GeV provides the best sensitivity. Figure 11 shows 95% exclusion contours in the the ∼ -plane, for an axion mass of 1 MeV. The exclusion does not depend significantly on the axion mass for masses up to at least 1 GeV. The limits on ∼ increase linearly with . For = 1 TeV, couplings ∼ above 0.008 are excluded. Expressed in terms of the ∼ / ratio, values above 8 × 10 −6 GeV −1 are excluded at 95% CL. As in the case of the dark energy and ADD models,  the validity of the effective field implementation of the model is challenged forˆ> 2 . For values of below 2 TeV, the signal yields are reduced significantly when applying a suppressing weighting factor 4 /ˆ2 for events withˆ> 2 . The effect is reduced to about 5% for = 2 TeV and it is negligible for above 3 TeV.

Invisibly decaying Higgs boson
The results are interpreted in terms of 95% CL upper limits on the branching ratio for an invisibly decaying Higgs boson. The signal yields are dominated by gluon-gluon fusion production processes (about 73%), followed by the contributions from VBF (18%), (8%), and¯+ (1%) processes. The low miss T region plays an important role in enhancing the sensitivity of the data to the Higgs signal and the full miss T spectrum is employed in computing the limits. The observed agreement between data and the SM background predictions in the measured miss T distribution leads to a 95% CL observed (expected) exclusion limit on the invisible branching ratio of the Higgs boson of 0. 34 Figure 11: Observed and expected 95% CL upper limits on the coupling ∼ as a function of the effective scale for ALP mass of 1 MeV. The bands indicate the ±1 theory uncertainties in the observed limit and the ±1 and ±2 ranges of the expected limit in the absence of a signal. The 95% CL limits are computed with no suppression of the events withˆ> 2 .

Conclusions
Results are reported from a search for new phenomena in events with an energetic jet and large missing transverse momentum in proton-proton collisions at √ = 13 TeV at the LHC, based on data corresponding to an integrated luminosity of 139 fb −1 collected by the ATLAS detector during 2015-2018. Compared to previous publications, in addition to an increase of almost a factor of four in the data size, the analysis implements a number of improvements in the signal selection and the background determination leading to enhanced sensitivity. The measurements are in agreement with the SM predictions. The results are translated into model-independent 95% CL upper limits on the visible cross section for new phenomena, and these range from 736 fb to 0.3 fb with increasing missing transverse momentum. Improved bounds on the parameters for a variety of models for new phenomena have been derived. In the case of simplified models for WIMP-pair production in the -channel, with Dirac fermions as dark-matter candidates, an axial-vector mediator with masses below 2.1 TeV is excluded at 95% CL for very light WIMPs and coupling values = 1/4 and = 1. For the first time, the ATLAS monojet analysis reaches sensitivity for excluding pseudoscalar mediators with masses below 376 GeV, for very light WIMPs and coupling values = 1 and = 1.
Similarly, the results are interpreted in terms of a search for squark-pair production in a compressedmass supersymmetric scenario. In the case of stop-and sbottom-pair production with˜1 → +˜0 1 or 1 → + +˜0 1 and˜1 → +˜0 1 , respectively, squark masses below about 550 GeV and 550 GeV are excluded at 95% CL, thus surpassing previous exclusions by almost 100 GeV. In the case of squark-pair production with˜→ +˜0 1 ( = , , , ), squark masses below 925 GeV are excluded. The results are expressed in terms of 95% CL limits on the suppression scale 2 for the Horndeski dark-energy model with = 0.1 GeV and ≠2 = 0 , 2 = 1. Suppression scales 2 below about 1.5 TeV are excluded. In the case of the ADD model with large extra spatial dimensions, 95% CL lower limits on the fundamental Planck scale in 4 + dimensions vary in the range between 11.2 TeV and 5.9 TeV for = 2 and = 6, respectively. In models with axion-like particles with coupling to gluons, couplings-to-effective-scale ratios ∼ / above 8 × 10 −6 GeV −1 are excluded at 95% CL for axion masses up to 1 GeV. Finally, limits are obtained for the branching ratio of an invisibly decaying Higgs boson. Branching fractions above 0.34 are excluded at 95% CL. The ATLAS Collaboration