Searches for electroweak production of supersymmetric particles with compressed mass spectra in $\sqrt{s}=13$ TeV $pp$ collisions with the ATLAS detector

This paper presents results of searches for electroweak production of supersymmetric particles in models with compressed mass spectra. The searches use 139 fb$^{-1}$ of $\sqrt{s}=13$ TeV proton-proton collision data collected by the ATLAS experiment at the Large Hadron Collider. Events with missing transverse momentum and two same-flavor, oppositely charged, low transverse momentum leptons are selected, and are further categorized by the presence of hadronic activity from initial-state radiation or a topology compatible with vector-boson fusion processes. The data are found to be consistent with predictions from the Standard Model. The results are interpreted using simplified models of $R$-parity-conserving supersymmetry in which the lightest supersymmetric partner is a neutralino with a mass similar to the lightest chargino, the second-to-lightest neutralino or the slepton. Lower limits on the masses of charginos in different simplified models range from 193 GeV to 240 GeV for moderate mass splittings, and extend down to mass splittings of 1.5 GeV to 2.4 GeV at the LEP chargino bounds (92.4 GeV). Similar lower limits on degenerate light-flavor sleptons extend up to masses of 251 GeV and down to mass splittings of 550 MeV. Constraints on vector-boson fusion production of electroweak SUSY states are also presented.


Introduction
Extensions of the Standard Model (SM) that include new states with nearly degenerate masses can help to resolve open issues in particle physics while evading constraints from experiments at high-energy colliders. The mass spectra of such new states are referred to in this paper as "compressed". Supersymmetry (SUSY) [1][2][3][4][5][6] predicts new particles that have identical quantum numbers to their SM partners with the exception of spin, with SM fermions having bosonic partners and SM bosons having fermionic partners. The neutralinos χ 0 1,2,3,4 and charginos χ ± 1,2 are collectively referred to as electroweakinos, where the subscripts indicate increasing electroweakino mass. If the χ 0 1 is stable, e.g. as the lightest SUSY partner (LSP) in R-parity-conserving SUSY models [7], then it is a viable dark-matter candidate [8,9]. In the compressed SUSY models considered in this paper, the χ 0 1 is close in mass to a heavier SUSY partner such as a chargino ( χ ± 1 ), second-lightest neutralino ( χ 0 2 ), or slepton ( , the SM lepton partner). This paper presents searches for physics beyond the SM in signatures sensitive to models with compressed mass spectra. Simplified SUSY models [10][11][12] are used to optimize the searches and interpret the results. The searches use 13 TeV pp collision data corresponding to 139 fb −1 of integrated luminosity, collected by the ATLAS experiment [13] from 2015 to 2018 at the CERN Large Hadron Collider (LHC).
All searches assume pair production of SUSY particles via electroweak interactions, with subsequent decays into the χ 0 1 and SM particles. The electroweakino mass eigenstates are a mixture of wino, bino, and higgsino fields,1 which form the SUSY partners of the SM W, γ/Z, and Higgs fields, respectively. In the minimal supersymmetric extension of the SM (MSSM) [14,15] the masses of the bino, wino, and higgsino states are parameterized in terms of M 1 , M 2 , and µ, respectively. For large values of tan(β), these three parameters drive the phenomenology of the electroweakinos.
Four SUSY scenarios are considered in the interpretation of the searches. In the first scenario, the lightest SUSY partners are assumed to be a triplet of higgsino-like states ( χ 0 1 , χ ± 1 , χ 0 2 ), in which the mass-splitting between the states is partially determined by the magnitude of M 1 or M 2 relative to | µ|. Such a scenario, referred to here as higgsino models, is motivated by naturalness arguments [16,17], which suggest that | µ| should be near the weak scale [18][19][20][21] while M 1 and/or M 2 can be larger.
The second scenario features a similar particle spectrum to the first, except with |M 1 | < |M 2 | | µ|, so that the produced electroweakinos have wino and/or bino nature. In such wino/bino scenarios the LSP can be a thermal-relic dark-matter candidate that was depleted in the early universe through coannihilation processes to match the observed dark-matter density [22,23]. The production cross-section in such scenarios is typically larger than in the first scenario. They are also poorly constrained by dark-matter direct-detection experiments, and collider searches constitute the only direct probe for | µ| > 800 GeV [24]. Diagrams representing the production mode for the first two scenarios are shown in Figure 1(a). A χ 0 2 produced in either scenario can decay into a dilepton pair via an off-shell Z boson (Z * ), such that the dilepton invariant mass m is kinematically restricted to be smaller than the mass-splitting between the χ 0 2 and χ 0 1 . Hadronic initial-state radiation (ISR) is also required to boost the system as a way of enhancing the sensitivity of the search.
The third scenario is similar to the previous two, but it instead assumes that the pair production of the electroweakinos proceeds via vector-boson fusion (VBF) processes, in which SM weak bosons exchange an electroweakino in a t-channel process to produce two electroweakinos and a pair of forward jets. Such  Figure 1: Diagrams representing the two-lepton final state of (a) production of electroweakinos χ 0 2 χ ± 1 with initial-state radiation ( j), (b) VBF production of electroweakinos χ 0 2 χ ± 1 , and (c) slepton pair ( ) production in association with initial-state radiation ( j). The higgsino simplified model also considers χ 0 2 χ 0 1 and χ + 1 χ − 1 production.
scenarios typically have very low cross-sections, but can complement the sensitivity of qq annihilation modes that dominate the inclusive higgsino and wino/bino cross-sections, especially for LSP masses above a few hundred GeV [25]. An example of such a process is illustrated in Figure 1(b). The kinematic cutoff of the m distribution is also used as the primary discriminant in this scenario, along with the presence of two forward jets consistent with a VBF production mode.
The fourth scenario assumes the presence of scalar partners of the SM leptons (slepton, ) that are slightly heavier than a bino-like LSP. Such models can explain dark-matter thermal-relic densities through coannihilation channels, as well as the muon g − 2 anomaly [26,27]. This process is illustrated in Figure 1(c). This scenario exploits the relationship between the lepton momenta and the missing transverse momentum through the stransverse mass, m T2 [28,29], which exhibits a kinematic endpoint similar to that for m in electroweakino decays.
Events with two same-flavor opposite-charge leptons (electrons or muons), significant missing transverse momentum of size E miss T , and hadronic activity are selected for all scenarios. Signal regions (SRs) are defined by placing additional requirements on a number of kinematic variables. The dominant SM backgrounds are either estimated with in situ techniques or constrained using data control regions (CRs) that enter into a simultaneous likelihood fit with the SRs. The fit is performed in bins of either the m distribution (for electroweakinos) or the m T2 distribution (for sleptons).
Constraints on these compressed scenarios were first established at LEP [30][31][32][33][34][35][36][37][38][39][40]. The lower bounds on direct chargino production from these results correspond to m( χ ± 1 ) > 103. 5 GeV for ∆m( χ ± 1 , χ 0 1 ) > 3 GeV and m( χ ± 1 ) > 92.4 GeV for smaller mass differences, although the lower bound on the chargino mass weakens to around 75 GeV for models with additional new scalars and higgsino-like cross-sections [41]. For sleptons, conservative lower limits on the mass of the scalar partner of the right-handed muon, denoted µ R , are approximately m( µ R ) 94. 6 GeV for mass splittings down to m( µ R ) − m( χ 0 1 ) 2 GeV. For the scalar partner of the right-handed electron, denoted e R , LEP established a universal lower bound of m( e R ) 73 GeV that is independent of ∆m( e R , χ This paper extends previous LHC results by increasing the integrated luminosity, extending the search with additional channels, and exploiting improvements in detector calibration and performance. The dedicated search for production via VBF is also added and the event selection was reoptimized and uses techniques based on Recursive Jigsaw Reconstruction [46], which improve the separation of the SUSY signal from the SM backgrounds.

ATLAS detector
The ATLAS experiment is a general-purpose particle detector that surrounds the interaction point with nearly 4π solid angle coverage.2 It comprises an inner detector, calorimeter systems, and a muon spectrometer. The inner detector provides precision tracking of charged particles in the pseudorapidity region |η| < 2.5, consisting of pixel and microstrip silicon subsystems within a transition radiation tracker. The innermost pixel detector layer, the insertable B-layer [47,48], was added for √ s = 13 TeV data-taking to improve tracking performance. The inner detector is immersed in a 2 T axial magnetic field provided by a superconducting solenoid. High-granularity lead/liquid-argon electromagnetic sampling calorimeters are used for |η| < 3.2. Hadronic energy deposits are measured in a steel/scintillator tile barrel calorimeter in the |η| < 1.7 region. Forward calorimeters cover the region 3.2 < |η| < 4.9 for both electromagnetic and hadronic measurements. The muon spectrometer comprises trigger and high-precision tracking chambers spanning |η| < 2.4 and |η| < 2.7, respectively, with a magnetic field provided by three large superconducting toroidal magnets. Events of interest are selected using a two-level trigger system [49], consisting of a first-level trigger implemented in hardware, which is followed by a software-based high-level trigger.

Data and simulated event samples
Events were selected with a E miss T trigger, employing varied trigger thresholds as a function of the data-taking periods. The trigger is > 95% efficient for offline E miss T values above 200 GeV for all periods. The dataset used corresponds to 139 fb −1 of √ s = 13 TeV pp collision data, where the uncertainty in the integrated luminosity is 1.7% [50], obtained using the LUCID-2 detector [51] for the primary luminosity measurements. The average number of interactions per bunch-crossing was 33.7.
Samples of Monte Carlo (MC) simulated events are used to estimate the signal yields, and for estimating the background from processes with prompt leptons, as well as in the determination of systematic uncertainties.
For the first signal scenario introduced in Section 1, samples were generated for a simplified model of higgsino LSPs, including production of χ − 1 χ + 1 , χ 0 2 χ ± 1 and χ 0 2 χ 0 1 . The masses of the neutralinos ( χ 0 1,2 ) were varied while the chargino mass was set to χ ± 1 = 1 2 m( χ 0 1 ) + m( χ 0 2 ) . Mass splittings in the case of pure higgsinos are generated by radiative corrections, and are of the order of hundreds of MeV [52]. Mass splittings of the order of tens of GeV can be obtained by introducing mixing with wino or bino states. In this simplified model, mass differences ranging from 1 GeV to 60 GeV are considered, but the calculated cross-sections assume electroweakino mixing matrices corresponding to pure higgsino 2 ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the center of the detector and the z-axis along the beam pipe. The x-axis points from the IP to the center of the LHC ring, and the y-axis points upwards. Cylindrical coordinates (r, φ) are used in the transverse plane, φ being the azimuthal angle around the z-axis. The pseudorapidity is defined in terms of the polar angle θ as η = − ln tan(θ/2). Angular distance is measured in units of ∆R ≡ (∆η) 2 + (∆φ) 2 . Rapidity is defined by y = 1 2 ln[(E + p z )/(E − p z )], where E is the energy and p z is the longitudinal component of the momentum along the beam direction. χ 0 2 , χ ± 1 and χ 0 1 states, and all other SUSY particles are decoupled. Typical values of cross-sections for m( χ 0 2 ) = 110 GeV and m( χ 0 1 ) = 100 GeV are 4.3 ± 0.1 pb for χ 0 2 χ ± 1 production, 2.73 ± 0.07 pb for χ 0 2 χ 0 1 production, and 2.52 ± 0.08 pb for χ + 1 χ − 1 production. The samples were generated at leading order (LO) with MG5_aMC@NLO 2.6.1 [53] using the NNPDF23LO [54] parton distribution function (PDF) set and included up to two extra partons in the matrix element (ME). The electroweakinos were decayed with M S [55]. The events were then interfaced with P 8.212 [56] to model the parton shower (PS), hadronization, and underlying event (UE) using the A14 set of tuned parameters (tune) [57]. The ME-PS matching was performed using the CKKW-L scheme [58] with the merging scale set to 15 GeV. To enforce an ISR topology, at least one parton in the final state was required to have a transverse momentum (p T ) greater than 50 GeV. Possible diagrams including colored SUSY particles were excluded from the generation.
In the wino/bino scenario, the generated process is pp → χ 0 2 χ ± 1 . The χ 0 1 is a pure bino state, with the χ 0 2 and χ ± 1 states forming degenerate pure wino states. The generator configurations are consistent with those used for the higgsino samples. A typical value of the χ 0 2 χ ± 1 production cross-section is 16.0 ± 0.5 pb for m( χ 0 2 ) = m( χ ± 1 ) = 110 GeV. Additional samples were generated for the third scenario of pair production of electroweakinos produced via VBF. These were generated with the same decay, PS, hadronization, and UE configuration as the higgsino simplified model samples. The ME generation was the same as in the higgsino case, but used an updated version of MG5_aMC@NLO (version 2.6.2). In order to select uniquely the VBF topologies, the number of QCD vertices was set to zero. An additional filter was applied to select events with exactly two parton emissions in the ME. The invariant mass of the two partons is required to be at least 200 GeV, while the minimum transverse momentum of each parton is 12 GeV. Typical values of LO cross-sections with these requirements for m( χ 0 2 ) = 100 GeV and m( χ 0 1 ) = 90 GeV are 16 ± 1 fb and 47 ± 4 fb, for the higgsino and wino/bino models, respectively. For higgsino masses smaller than half of the Higgs boson mass, the cross-sections include contributions from VBF Higgs production with decays h → χ 0 2 χ 0 1 . The electroweakino searches exploit the kinematic endpoint in the dilepton invariant mass spectrum from the decay chain χ 0 2 → Z * χ 0 1 , Z * → . Therefore, processes that involve the production of a χ 0 2 neutralino dominate the sensitivity of the search. The branching ratios for the processes χ 0 2 → Z * χ 0 1 and χ ± 1 → W * χ 0 1 were fixed to 100% for all the scenarios given above. The branching ratios of Z * → and W ± * → ν depend on the invariant mass of the off-shell vector boson. For both the higgsino and wino/bino models, the branching ratios were computed with SUSY-HIT 1.5a [59], which accounts for finite b-quark and τ-lepton masses. At ∆m χ 0 2 , χ 0 1 = 40 GeV the Z * → branching ratio to electrons or muons is 3.5%. This increases to 5.3% and 5.0%, respectively, at ∆m χ 0 2 , χ 0 1 = 1 GeV as decays into heavier quarks or τ-leptons become kinematically inaccessible. Similarly, for W * → ν the branching ratios to electrons or muons are both 11% at a mass splitting of 40 GeV, but increase to 20% and 17%, respectively, for ∆m χ 0 2 , χ 0 1 = 1 GeV. The distribution of the dilepton invariant mass from the decay of the virtual Z * [60] depends on the relative sign of the χ 0 1 and χ 0 2 mass parameters. In a pure higgsino model the product of the signed mass eigenvalues m χ 0 2 × m χ 0 1 can only be negative, while for the wino/bino case either positive or negative products are allowed.3 The generated wino/bino process assumes the product of the signed mass eigenvalues is positive, and the analytical description of the expected lineshape is used to reweight the m distribution : Dilepton invariant mass for higgsino and wino/bino simplified models. The endpoint of the distribution is determined by the difference between the masses of the χ 0 2 and χ 0 1 . The results from simulation (histograms) are compared with analytic calculations of the expected lineshape (dashed lines) presented in Ref. [60]. The product of the signed mass eigenvalues m χ 0 2 × m χ 0 1 is negative for the higgsino model and can be either negative or positive for wino/bino scenarios.
to the case of the product being negative. The difference between wino/bino and higgsino lineshapes, as well as the level of agreement between the reweighted distribution and the expected lineshape, is shown in Figure 2. The two possible wino/bino m distributions are used to provide two separate model-dependent interpretations of the results. With the exception of the signal modeling, the interpretations for higgsino and both wino/bino samples are otherwise conducted identically, and use the same search regions as defined in Section 5.
For the fourth scenario, samples with direct production of selectrons e L, R or smuons µ L, R were generated. The L, R subscripts denote left-or right-handed chirality of the corresponding SM lepton partners. All sleptons flavors and chirality contributions are assumed to be degenerate in mass. A typical value of the slepton production cross-section is 0.55 ± 0.01 pb for m( L, R ) = 110 GeV. These particles decay with a 100% branching ratio into their corresponding SM partner lepton and a pure bino neutralino, χ 0 1 . The slepton samples were generated with MG5_aMC@NLO 2.6.1 and interfaced with P 8.230. The PDF set used was NNPDF2.3LO with the A14 tune. Similar to the higgsino and wino/bino samples, CKKW-L merging [58] was used for the ME-PS matching, with the merging scale set to a quarter of the slepton mass.
Cross-sections for all but the VBF signal scenarios are calculated with R 2.0.1 at NLO+NLL precision [63][64][65][66][67][68][69][70]. The VBF cross-sections are computed at LO precision with MG5_aMC@NLO 2.6.2. The evaluation of the cross-sections and corresponding uncertainty are taken from an envelope of cross-section predictions using different PDF sets, and varied factorization and renormalization scales. This procedure is described in Ref. [71], and is the same procedure as used in the previous search [45].
The SM background processes are estimated from a combination of MC simulation as well as data-driven approaches. The latter are described in Section 6. S 2.2.1 and 2.2.2 [72] were used to model the V+jets (V = W, Z, γ * ) samples involving leptonically decaying vector bosons, as well as diboson (WW, Z Z and W Z, collectively referred to as VV), and fully leptonic triboson processes. The Z ( * ) /γ * + jets and VV samples provide coverage of dilepton invariant masses down to 0.5 GeV for Z ( * ) /γ * → e + e − /µ + µ − , and 3.8 GeV for Z ( * ) /γ * → τ + τ − . A separate set of Z(→ µµ)+jets samples were generated using MG5_aMC@NLO using the same configuration as for the signal samples described above in order to evaluate initial-and final-state radiation modeling in signal samples. Gluon-gluon fusion (ggF) and VBF single-Higgs production were generated with P -B [73], while Higgs production in association with a massive vector boson was generated with P 8.186, and tth production was generated with MG5_aMC@NLO 2.2.3. P -B was used to generate tt [73][74][75][76], single top [77] and top quarks produced in association with W bosons [78]. Rarer top-quark processes all used MG5_aMC@NLO (versions 2.2.2/2.3.3). Matrix elements, excluding those generated with P or S , were then interfaced with P 8 using the ME+PS prescription. Further details on the configuration of the simulation of SM processes can be found in Refs. [79][80][81][82][83]. A summary of the generator configurations, including the PDF sets and the order of the cross-section calculations used for normalization, is given in Table 1.
To simulate the effects of additional pp collisions, referred to as pileup, in the same and neighboring bunch crossings, additional interactions were generated using the soft QCD processes of P 8.186 with the A3 tune [96] and the MSTW2008LO PDF set [97], and were overlaid onto each simulated hard-scatter event. The MC events were reweighted to match the pileup distribution observed in the data.
Background and signal samples made use of E G 1.6.0 and 1.2.0 [98] to model the decay of bottom and charm quarks, with the exception of the background samples modeled with S . All MC simulated samples were processed through the ATLAS simulation framework [99] in G 4 [100]. The samples for the signal scenarios made use of the ATLAS fast simulation, which parameterizes the response of the calorimeters.

Event reconstruction
Events are required to have at least one reconstructed pp interaction vertex with a minimum of two associated tracks with p T > 500 MeV. In events with multiple vertices, the primary vertex is defined as the one with the highest p 2 T of associated tracks. To reject events with detector noise or noncollision backgrounds, a set of basic quality criteria [101] are applied.
Leptons, jets and tracks are "preselected" using loose identification criteria, and must survive tighter "signal" identification requirements in order to be selected for the search regions. Preselected leptons and jets are used in fake/nonprompt (FNP) lepton background estimates, as well as in resolving ambiguities between tracks and clusters associated with multiple lepton and jet candidates.
Isolation criteria are used in the definition of signal leptons, and are based on tracking information, calorimeter clusters, or both. Isolation energies are computed as a p T of nearby activity, excluding the contributions from nearby leptons, and are effective in reducing contributions from semileptonic heavy-flavor hadron decays and jets faking prompt leptons. The isolation requirements used in this analysis are based on those described in Refs. [102] and [103], with updates to improve their performance under the increased pileup conditions encountered in the 2017 and 2018 data samples.
Electrons are required to have p T > 4.5 GeV and |η| < 2.47. Preselected electrons are further required to pass the calorimeter-and tracking-based VeryLoose likelihood identification [103], and to have a longitudinal impact parameter z 0 relative to the primary vertex that satisfies |z 0 sin θ| < 0.5 mm. Signal electrons must satisfy the Medium identification criterion [103], and be compatible with originating from the primary vertex, with the significance of the transverse impact parameter defined relative to the beam position satisfying |d 0 |/σ(d 0 ) < 5. Signal electrons are further refined using the Gradient isolation working point [103], which uses both tracking and calorimeter information.
Muons are required to satisfy p T > 3 GeV and |η| < 2.5. Preselected muons are identified using the LowPt criterion [104], a reoptimized selection similar to those defined in Ref. [102] but with improved signal efficiency and background rejection for p T < 10 GeV muon candidates. The LowPt working point has improved efficiency for muons with p T < 4 GeV traversing the central detector region, which can lose enough energy in the calorimeters that they do not reach the second station of precision muon tracking chambers. The LowPt selection accepts candidates composed of track segments in the inner detector matched to track segments from a single station of the muon spectrometer. Misidentified muon candidates originating from in-flight hadron decays are rejected by requirements on the significance of a change in trajectory along the track, and by requiring that the momentum measurements in the inner tracker and in the muon spectrometer are compatible with each other. For prompt muons with 3 < p T < 6 GeV, the LowPt criterion recovers approximately 20% of the identification efficiency in the |η| < 1.2 region, while maintaining an average misidentification probability comparable to the Medium selection described in Ref. [102].
Preselected jets are reconstructed from calorimeter topological energy clusters [105] in the region |η| < 4.5 using the anti-k t algorithm [106, 107] with radius parameter R = 0.4. The jets are required to have p T > 20 GeV after being calibrated in accord with Ref. [108] and having the expected energy contribution from pileup subtracted according to the jet area [109]. In order to suppress jets due to pileup, jets with p T < 120 GeV and |η| < 2.5 are required to satisfy the Medium working point of the jet vertex tagger [109], which uses information from the tracks associated with the jet. The Loose working point of the forward jet vertex tagger [110] is in turn used to suppress pileup in jets with p T < 50 GeV and |η| > 2.5. From the sample of preselected jets, signal jets are selected if they satisfy p T > 30 GeV and |η| < 2.8. The VBF search uses a modified version of signal jets, labeled VBF jets, satisfying p T > 30 GeV and |η| < 4.5.
Jets identified as containing b-hadron decays, referred to as b-tagged jets, are identified from preselected jets within |η| < 2.5 using the MV2c10 algorithm [111]. The p T > 20 GeV requirement is maintained to maximize the rejection of the tt background. The b-tagging algorithm working point is chosen so that b-jets from simulated tt events are identified with an 85% efficiency, with rejection factors of 2.7 for charm-quark jets and 25 for light-quark and gluon jets.
The following procedure is used to resolve ambiguities between the reconstructed leptons and jets. It employs the distance measure ∆R y = (∆y) 2 + (∆φ) 2 , where y is the rapidity. Electrons that share an inner detector track with a muon candidate are discarded to remove bremsstrahlung from muons followed by a photon conversion. Non-b-tagged jets that are separated from the remaining electrons by ∆R y < 0.2 are removed. Jets containing a muon candidate within ∆R y < 0.4 and with fewer than three tracks with p T > 500 MeV are removed to suppress muon bremsstrahlung. Electrons or muons with ∆R y < 0.4 from surviving jet candidates are removed to suppress bottom and charm hadron decays.
Signal regions based on a signal lepton and an isolated low-p T track are used to increase the efficiency for electroweakino signals with the lowest mass splittings, where the lepton p T can be very low. For these regions the track is selected to be matched to a reconstructed electron or muon candidate with no identification requirements, including muons reconstructed with the CaloTagged and SegmentTagged algorithms described in Ref. [102]. Preselected tracks with p T > 500 MeV and η < 2.5 are selected using the Tight-Primary working point defined in Ref. [112]. Signal tracks are required to be within ∆R = 0.01 of a reconstructed electron or muon candidate. Electron (muon) candidates can be reconstructed with transverse momenta as low as 1 (2) GeV, and are required to fail the signal lepton requirements defined above to avoid any overlap. Signal tracks with p T that differs from the transverse momentum of the matched lepton by more than 20% are rejected. The track-lepton matching allows the tracks to be identified as electron or muon tracks, reducing backgrounds from tracks not originating from the leptonic decay of a SUSY particle. Signal tracks must also satisfy dedicated isolation criteria: they are required to be separated from preselected jets by at least ∆R > 0.5, and the p T of preselected tracks within ∆R = 0.3 of signal tracks, excluding the contributions from nearby leptons, is required to be smaller than 0.5 GeV. Finally, signal tracks must satisfy p T > 1 GeV, |z 0 sin θ| < 0.5 mm and |d 0 |/σ(d 0 ) < 3.
The missing transverse momentum p miss T , with magnitude E miss T , is defined as the negative vector sum of the transverse momenta of all preselected objects (electrons, muons, jets, and photons [103]), and an additional soft term that is constructed from all tracks that are not associated with any lepton or jet, but that are associated with the primary vertex. A dedicated overlap removal procedure is used to resolve ambiguities between the reconstructed objects [113]. In this way, E miss T is adjusted for the best calibration of jets and leptons, while maintaining pileup independence in the soft term [114].
Small scale factors are applied to the efficiencies of reconstructed electrons, muons, b-tagged jets, and tracks in the simulated samples to match the reconstruction efficiencies in data. The scale factors for b-tagged jets account for the differences between data and simulated samples in the identification efficiencies for jets, including b-hadron decays, as well as misidentification rates of jets initiated from charm quarks, light-flavor quarks, or gluons. The scale factors for low-momentum leptons are obtained from J/ψ → ee/µµ events with the same tag-and-probe methods as used for higher-p T electrons [103] and muons [102]. The scale  factors used to account for track-lepton matching efficiency differences between data and simulation are derived from events with a J/ψ meson decaying into a low-p T signal lepton and a preselected track. The track-isolation scale factors are measured using events with a Z boson decaying into a signal lepton and a track matched to a reconstructed lepton candidate. All track scale factors are found to be compatible with 1.
After all lepton selection criteria and efficiency scale factors are applied, the efficiency for reconstructing and identifying signal electrons within the detector acceptance in the higgsino and slepton signal samples ranges from 20% for p T = 4.5 GeV to over 75% for p T > 30 GeV. The corresponding efficiency for signal muons ranges from approximately 50% at p T = 3 GeV to 90% for p T > 30 GeV. The efficiency of selecting signal tracks for electroweakino events peaks at 78% for tracks with p T = 2.5 GeV, with lower efficiencies at lower p T due to track selection criteria and at higher p T due to increasing electron and muon efficiencies. The efficiency for signal electrons, muons, and isolated tracks in a mix of slepton and higgsino samples is shown in Figure 3 as a function of lepton p T .
Dedicated scale factors are also used to re-weight MC events to properly model the trigger efficiency observed in data. These scale factors are measured in events selected with single-muon triggers, passing kinematic selections similar to the ones used to define the SRs. They are parameterized as a function of E miss T and found to vary between 0.85 and 1 in the E miss T range of interest. The uncertainty in the parameterization of the scale factors is negligible. An uncertainty of 5% is assigned to the scale factors to cover their dependence on other kinematic quantities of interest, such as m and m T2 . Additional > 120 > 120 uncertainties of at most 4% are assigned due to differences between the trigger efficiencies determined with MC events for the different signal and background processes.

Signal regions
Events entering into all SRs share a common preselection, with requirements listed in Table 2. The 2 channels require exactly two opposite-charge (OS) signal leptons of the same flavor, while the 1 1T channel requires exactly one signal lepton and at least one OS signal track of the same flavor. In events where more than one OS same-flavor signal track is present, the candidate with the highest p T is used to define the 1 1T system. In regions with two leptons, the higher-p T lepton is referred to as the "leading" lepton ( 1 ) while the lower-p T lepton is the "subleading" lepton ( 2 ).
Preselection requirements are employed to reduce backgrounds and form a basis for SRs and CRs used in the simultaneous fit. The leading lepton is required to have p T > 5 GeV, which reduces backgrounds from FNP leptons. Pairs of muons are required to be separated by ∆R µµ > 0.05, while pairs of electrons are required to be separated by ∆R ee > 0.3 to avoid reconstruction inefficiencies due to overlapping electron showers in the EM calorimeter. Electrons and muons are likewise required to be separated by ∆R eµ > 0.2 to avoid energy deposits from muons spoiling electron shower shapes. An additional requirement that m be outside of [3.0, 3.2] GeV removes contributions from J/ψ decays, while requiring m < 60 GeV reduces contributions from on-shell Z-boson decays. Contributions from other hadronic resonances, e.g. Υ states, are expected to be negligible in the search regions and are not explicitly vetoed. Requirements on the minimum angular separation between the lepton candidates (∆R ) and invariant mass (m ) remove events in which an energetic photon produces collinear lepton pairs.
The m ττ variable [115][116][117] approximates the invariant mass of a leptonically decaying τ-lepton pair Table 3: Requirements applied to events entering into the four signal regions used for electroweakino searches. The 1 1T preselection requirements from Table 2 are implied for SR-E-1 1T, while the 2 ones are implied for the other SRs.
if both τ-leptons are sufficiently boosted so that the neutrinos from each τ decay are collinear with the visible lepton momentum. It is defined as m ττ = sign m 2 ττ m 2 ττ , which is the signed square root of where p 1 and p 2 are the lepton four-momenta, while the parameters ξ 1 and ξ 2 are determined by solving p miss T = ξ 1 p 1 T + ξ 2 p 2 T . It can be less than zero in events where one of the lepton momenta has a smaller magnitude than the E miss T and points in the hemisphere opposite to the p miss T vector. Events with 0 < m ττ < 160 GeV are rejected, which reduces backgrounds from Z → ττ and has an efficiency greater than 80% for the signals considered.
The reconstructed E miss T is required to be greater than 120 GeV in preselection, with higher thresholds applied in some SRs. For SUSY events in which much of the invisible momentum is carried by the χ 0 1 pair, these requirements on E miss T suggest that the SUSY system is recoiling against additional hadronic activity, either in the form of ISR or the forward jets in VBF processes. All events are therefore required to have at least one jet with p T > 100 GeV. Additional jets in the event are also required to be separated from the p miss T by min(∆φ(any jet, p miss T )) > 0.4 in order to suppress the impact of jet energy mismeasurement on E miss T . For searches involving ISR, the leading jet is required to be separated from the p miss T by at least 2.0 radians in φ. In the 2 channel, events with one or more b-tagged jets with p T > 20 GeV (N 20 b-jet ) are vetoed to reduce backgrounds from tt production.
After applying the preselection requirements above, SRs are further optimized for specific SUSY scenarios. Three categories of SRs, labeled SR-E, SR-VBF and SR-S, are constructed: the first for electroweakinos recoiling against ISR (or simply electroweakinos), the second for electroweakinos produced through VBF, and the last targeting sleptons recoiling against ISR.
The SRs designed for optimal sensitivity to electroweakinos are defined in Table 3. High-E miss T regions, labeled SR-E-high and SR-E-1 1T, require E miss T > 200 GeV, where the online E miss T triggers are fully efficient for the SUSY signal. Low-E miss T regions are constructed using events with 120 GeV < E miss T < 200 GeV: SR-E-med targets electroweakinos with small mass splittings and SR-E-low targets mass splittings larger than ∼10 GeV.
The p T threshold for the subleading lepton is defined with sliding cuts that retain efficiency for soft leptons from low-∆m signals, while reducing backgrounds from FNP leptons in events with larger values of m . The sliding requirement was optimized using a significance metric separately in each SR, considering signal models with a variety of masses and mass splittings. The significance was calculated following In events with high-p T ISR jets, the axis of maximum back-to-back p T , referred to here as the thrust axis, approximates the direction of the recoil of the ISR activity against the sparticle pair. The recursive jigsaw reconstruction (RJR) technique [46] is used to divide each event into two hemispheres perpendicular to the thrust axis: a supersymmetric-particles hemisphere S, expected to contain the decay products of the electroweakinos or slepton pair and therefore the E miss T ; and an ISR hemisphere, containing hadronic activity. This bisection allows the calculation of two discriminating variables that are useful in isolating events with ISR-induced E miss T topologies: R ISR , the ratio of the E miss T to the transverse momentum of the ISR system, and M S T , the transverse mass of the S system. The R ISR variable in particular is sensitive to the mass splitting, with values near 1.0 for the most compressed SUSY events. Figure 4 shows the relationship between R ISR and m and m 100 T2 , which is exploited in SR-E-high and SR-S-high (m 100 T2 and SR-S-high are defined below) through sliding requirements on R ISR . increases due to the larger mass splitting. The 1 1T channel targets SUSY signals with especially low values of ∆m, which produce decay products with very low momentum. The signal region SR-E-1 1T therefore requires that the identified lepton has p T < 10 GeV and that the track has p T < 5 GeV. The lepton is also required to be within 1.0 radians of the p miss T in φ, to reduce backgrounds with tracks associated with nonprompt leptons or hadrons. Finally, the Table 4: Requirements applied to all events entering into signal regions used for searches for electroweakinos produced through VBF. The 2 preselection requirements from Table 2 are implied.

Variable
VBF SR Requirements Signal regions designed for sensitivity to electroweakinos produced through VBF are defined in Table 4 and denoted SR-VBF. VBF production is commonly characterized by the presence of two energetic jets with large dijet invariant mass and large separation in pseudorapidity. Two regions are constructed, distinguished by the pseudorapidity gap between the two leading jets: events with 2 < ∆η j j < 4 are tested in SR-VBF-low, while events with ∆η j j > 4 are tested in SR-VBF-high. The E miss T is required to be greater than 150 GeV, which increases the acceptance relative to an E miss T > 200 GeV requirement while not introducing significant additional backgrounds. Additional requirements on p 2 T , m 1 T , and E miss T /H lep T similarly reduce backgrounds for small losses in signal efficiency. The R VBF variable is constructed similarly to R ISR , with the vector sum of the two leading VBF jets in R VBF taking the place of the ISR system in R ISR . Additionally, in the case that an energetic jet is well separated from the two leading VBF jets, this jet is added to the decay tree. This forms an effective third-jet veto by altering the decay hemisphere, spoiling the back-to-back configuration in QCD-initiated events, while in signal events the central hadronic activity is expected to be suppressed. The R VBF variable is also sensitive to the mass splitting, so sliding requirements on R VBF are used in both VBF SRs. The acceptance times efficiency of higgsinos with m( χ 0 2 ) = 100 GeV and m( χ 0 1 ) = 95 GeV produced through VBF in the SR-VBF is 2.9 × 10 −4 .
The SRs designed to provide sensitivity for slepton production, denoted SR-S, are defined in Table 5. The slepton search exploits the relationship between the mass splitting and the lepton and E miss T kinematics via the stransverse mass (m T2 ) variable [28,29]. The stransverse mass is defined as: where m χ is the hypothesized mass of the invisible particles, and the transverse momentum vector q T with magnitude q T is chosen to minimize the larger of the two transverse masses, defined by The binned m and m 100 T2 distributions are used in two different types of statistical tests. The first test is a search for excesses with minimal model dependence, in which any given fit considers a single inclusive SR. An inclusive electroweakino SR is constructed by merging all SR-E-high, SR-E-med, SR-E-low, and SR-E-1 1T bins below a m bin boundary listed above, with each 2 electroweakino bin boundary corresponding to an inclusive SR. Similarly, the inclusive slepton regions are constructed by merging all SR-S-high and SR-S-low bins below the m 100 T2 bin boundaries. The inclusive VBF SRs are also constructed by merging the SR-VBF-low and SR-VBF-high bins below the m boundaries. Additional inclusive VBF SRs are defined using events in SR-VBF-high only.
The second type of test is referred to as an exclusion fit, which considers all relevant bins separately in the likelihood. Dielectron and dimuon events in the 2 electroweakino SRs and in the slepton SRs are also fitted separately in the exclusion fits.

Background estimation
The sources of SM background in regions with two leptons can be subdivided into two categories: reducible backgrounds from events where at least one of the candidate leptons is FNP, and irreducible backgrounds from events that contain two prompt leptons.
Since MC simulation is not expected to model processes with FNP leptons accurately, a data-driven method, referred to as the Fake Factor method [119, 120], is employed to estimate these backgrounds. The yields obtained from this procedure are cross-checked in validation regions (VRs), which are not used to constrain the fit and are orthogonal in selection to the CRs and SRs.
The dominant sources of irreducible background are tt/tW, WW/W Z, and Z ( * ) /γ * (→ ττ) + jets. These backgrounds are estimated using MC simulations normalized to data in dedicated CRs. Events originating from the production of a Drell-Yan lepton pair, triboson, Higgs boson or top quarks in association with gauge bosons constitute a small fraction of the total background. Their contributions in the regions with two leptons are estimated using the MC samples listed in Table 1. Additional VRs are used to validate the extrapolation of background in the fitting procedure within the same kinematic regime as the SRs.
The definitions of the CRs and VRs used in the electroweakino, VBF and slepton searches are summarized in Tables 6, 7 and 8, respectively. The VRSS regions are further described in Section 6.1, in the context of the FNP background estimation, while the remaining CRs and VRs are explained in Section 6.2.
The dominant source of background in the 1 1T channel is combinatorial, from events containing one prompt lepton and one random track, and is collectively estimated using data, as described in Section 6.3.

Reducible background in regions with two leptons
The FNP lepton background arises from jets misidentified as leptons, photon conversions, or semileptonic decays of heavy-flavor hadrons. Studies based on simulated samples indicate that the last is the dominant component in the SRs with two leptons. The contamination of the SRs by FNP lepton background is large at low values of m and m 100 T2 , and decreases at the upper end of the distributions. In the Fake Factor method, a two-lepton control sample is defined in data using leptons with modified signal lepton requirements. At least one of the leptons, labeled as anti-ID, is required to fail one or more of the requirements applied to signal leptons, but is required to satisfy less restrictive requirements. The other lepton can either meet all signal lepton requirements, in which case it is labeled as ID, or satisfy the anti-ID requirements. This sample is enriched in FNP lepton backgrounds and is therefore referred to as the FNP control sample. The contributions from processes with two prompt leptons in the FNP control Table 6: Definition of control ("CR" prefix) and validation ("VR" prefix) regions used for background estimation in the electroweakino search, presented relative to the definitions of the corresponding signal regions SR-E-high, SR-E-med and SR-E-low. The 2 preselection criteria from Table 2 and selection criteria from Table 3 are implied, unless specified otherwise.

Region
SR orthogonality Lepton Flavor Additional requirements Table 7: Definition of control ("CR" prefix) and validation ("VR" prefix) regions used for background estimation in the search for electroweakinos produced through VBF, presented relative to the definitions of the corresponding signal regions SR-VBF-high and SR-VBF-low. The 2 preselection criteria from Table 2 and selection criteria  from Table 4 are implied, unless specified otherwise.

Region SR orthogonality Lepton Flavor Additional requirements
Same sign ± ± ee + µe, µµ + eµ R VBF , m 1 T and p 2 T removed VRDF-VBF-low eµ + µe eµ + µe -VRDF-VBF-high eµ + µe eµ + µe - Table 8: Definition of control ("CR" prefix) and validation ("VR" prefix) regions used for background estimation in the slepton search, presented relative to the definitions of the corresponding signal regions SR-S-high and SR-S-low. The 2 preselection criteria from Table 2 and selection criteria from Table 5 are implied, unless specified otherwise.
Region SR orthogonality Lepton Flavor Additional requirements sample are subtracted using simulated samples. MC studies indicate that the leptons in the FNP control sample arise from processes similar to those for FNP leptons passing the SR selections. The FNP lepton background prediction in a given region is obtained by applying all selection requirements of that region to the FNP control sample and scaling each event by a weight assigned to each anti-ID lepton, referred to as the fake factor. Events in the FNP control sample containing a single anti-ID lepton have positive fake factors. Events with two anti-ID leptons receive a weight corresponding to the product of the weights for the two anti-ID leptons, and enter with opposite sign to correct for events with two FNP leptons.
The fake factor is measured in a data sample collected with prescaled low-p T single-lepton triggers. This sample is dominated by multijet events with FNP leptons and is referred to as the measurement sample. A selection of m 1 T < 40 GeV is applied to reduce the contributions from processes with prompt leptons in the measurement sample. The contributions from these processes are subtracted using MC simulation, with negligible impact on the measured fake factors.
To enrich the sample in FNP leptons similar to those contaminating the SRs, the leading-jet p T is required to be greater than 100 GeV. The fake factors are calculated as the ratio of ID to anti-ID leptons in the measurement sample, measured in bins of lepton p T , separately for electrons and muons. The fake factors are also found to have a dependence on the number of b-tagged jets in the events. Different fake factors are therefore computed in events with and without b-tagged jets.
The yields predicted by the Fake Factor method are cross-checked in dedicated VRs enriched in FNP lepton backgrounds, labeled VRSS. As summarized in Tables 6, 7 and 8, a dedicated VRSS is constructed for each SR by selecting events with two leptons with the same electric charge. The kinematic requirements applied to each VRSS are mostly the same as the ones used in the corresponding SR, ensuring the FNP lepton processes are similar in the two regions. To guarantee high purity in FNP lepton background, the selection criteria designed to suppress these processes in the SRs, such as the sliding cut on the p T threshold of the subleading lepton, are loosened or removed in each VRSS. The contribution of FNP background in the VRSS regions is typically above 91%, with the remaining backgrounds originating from VV processes with two prompt leptons of the same electric charge. The signal contamination is at most 14%.

Irreducible background in regions with two leptons
Several CRs are defined for the electroweakino, VBF and slepton searches, and are used to normalize the MC simulations of tt/tW and Z ( * ) /γ * (→ ττ) + jets background processes to the data in a simultaneous fit also including the SRs, as described in Section 8. In searches for electroweakinos and sleptons recoiling against ISR, CRs are also constructed to normalize the WW/W Z background. The event rates in the SRs are predicted by extrapolating from the CRs using the simulated MC distributions. This extrapolation is validated using events in dedicated VRs.
The CRs are designed to be statistically disjoint from the SRs, to be enriched in a particular background process, to have minimal contamination from the signals considered, and to exhibit kinematic properties similar to the SRs. The CRs labeled as CRtop are defined by selecting events with at least one b-tagged jet. The CRtop regions have purities ranging from 83% to 94% in processes with top quarks, and are used to constrain the normalization of the tt and tW processes with dilepton final states. The CRtau regions, which are enriched in the Z ( * ) /γ * (→ ττ) + jets process with purities of at least 75%, are constructed by selecting events satisfying m ττ ∈ [60, 120] GeV. Finally, the R ISR selection used to define the SRs is modified to construct CRs enriched in WW and W Z processes, denoted CRVV. In these CRs, 41%-45% of the events are VV events.
The tt/tW, WW/W Z and Z ( * ) /γ * (→ ττ) + jets processes containing two prompt leptons all yield sameflavor lepton pairs (ee and µµ) at the same rate as for different-flavor pairs (eµ and µe, where the first lepton is the leading lepton). This feature is used to enhance the statistical constraining power of the CRs, by selecting events with all possible flavor assignments (ee, µµ, eµ, and µe). It is also used to define additional VRs, denoted VRDF. One VRDF is defined for each 2 SR by requiring two different-flavor leptons (eµ and µe), but otherwise keeping the same kinematic selections as the corresponding SR. The relative fractions of each background process are similar in the SR and the corresponding VRDF. The signal contamination in the VRDF regions is at most 16%, originating from χ + 1 χ − 1 or χ 0 2 χ ± 1 higgsino events decaying fully leptonically.
In the search for electroweakinos recoiling against ISR, six single-bin CRs are defined as summarized in Table 6. Three CRs, labeled CR-E-high, employ a E miss T > 200 GeV selection and are used to constrain the normalization of tt/tW, WW/W Z and Z ( * ) /γ * (→ ττ) + jets backgrounds in SR-E-high. To minimize the impact of the mismodeling of the trigger efficiency in the simulation, three additional CRs, labeled CR-E-low, are defined by selecting events with E miss T ∈ [120, 200] GeV. These CRs are used to normalize the same background processes in SR-E-low. Events with FNP leptons entering the CRs are suppressed using the same sliding cut on p 2 T as the corresponding SRs. The dominant source of irreducible background in the SR-E-med region is the Z ( * ) /γ * (→ ττ) + jets process. It is difficult to construct a dedicated CR with enough events to constrain the normalization of the Z ( * ) /γ * (→ ττ) + jets background in the SR-E-med region. The CRtau-E-low region is therefore used for this purpose. The extrapolation from CRtau-E-low to SR-E-med is tested in an additional VR, labeled VRtau-E-med, defined by selecting events with m ττ ∈ [60, 120] GeV, but otherwise applying the same kinematic selections as in the SR-E-med region, as summarized in Table 6.
Two control regions are defined for the VBF search, as summarized in Table 7. The CRtop-VBF and the CRtau-VBF regions are designed with a ∆η j j > 2 requirement, and are used to constrain the normalizations of the tt/tW and Z ( * ) /γ * (→ ττ) + jets processes in both the SR-VBF-low and the SR-VBF-high regions. The number of events in the VBF CRs is increased by removing the m 1 T and R VBF selections used in the SRs.
Six CRs are used to normalize the tt/tW, WW/W Z and Z ( * ) /γ * (→ ττ) + jets background processes entering the SR-S-low and SR-S-high regions, as summarized in Table 8. The CRs used in the search for sleptons are designed similarly to the CRs used in the search for electroweakinos. One notable difference is the sliding cut on the p 2 T threshold, which is chosen to match the requirements used in the slepton SRs and therefore depends on m 100 T2 .

Background in the 1 1T signal region
The background in the SR-E-1 1T region is suppressed by requiring that the selected track be associated with a reconstructed lepton candidate. Simulation studies show that this background is dominated by events with one prompt lepton and one track from hadrons or nonprompt leptons. The MC samples used to model SM processes with two prompt leptons contribute negligibly in the 1 1T SR.
The amount of background in the 1 1T channel is estimated using a data-driven procedure. A control sample is defined in data with events that satisfy the same selection criteria as the SR-E-1 1T region. Instead of selecting OS events with one lepton and one track, the lepton and the track in the control sample are required to have the same electric charge (SS). The contamination of the SS control sample by signal is negligible. The data in the SS sample are directly used as the estimate of the background in SR-E-1 1T.
The background estimate assumes that the background events are produced with equal rates for OS and SS events. This is expected to be the case because the track is randomly selected and its electric charge is not correlated with the charge of the prompt lepton.
The assumption that OS and SS background events are produced with equal rates in the 1 1T signal region is tested in simulation using W+jets events. The ratio of OS to SS W+jets events was found to be compatible with one, with a statistical uncertainty of 12% determined by the size of the MC sample. A VR, denoted VR-1 1T, is constructed to test the assumption using data. The VR-1 1T is designed using the same kinematic selections as the 1 1T SR, except that ∆φ(lep, p miss T ) > 1.5 is required to ensure that the samples are disjoint. The upper bound on ∆R track used in SR-E-1 1T is removed to reduce the signal contamination, and the E miss T /H lep T requirement is loosened to E miss T /H lep T > 15 to increase the number of events in the VR. The kinematic distributions of the SS and OS data events in the VR-1 1T are compared and found to agree.

Systematic uncertainties
Systematic uncertainties are evaluated for all background processes and signal samples. As the predictions for the main SM background processes modeled via MC simulation are normalized to data in dedicated control regions, the systematic uncertainties only affect the extrapolation to the signal regions in these cases. Figure 5 illustrates the dominant classes of uncertainties in the expected background yields in the electroweakino, VBF and slepton SRs. The main sources of experimental uncertainty affect the FNP background predictions obtained with the Fake Factor method. These systematic uncertainties stem from the size of the FNP control samples, as well as from the size of the measurement sample used to compute the fake factors. The uncertainties associated with the subtraction of processes involving prompt leptons in the FNP control samples and in the measurement sample are estimated from simulation and found to be negligible. Uncertainties are also assigned to cover the differences in the event and lepton kinematics between the measurement region and the signal regions. Moreover, additional uncertainties are computed as the differences between the FNP background predictions and observed data in the VRSS regions.
Other sources of significant experimental systematic uncertainties are the jet energy scale (JES) and resolution (JER). The jet uncertainties are derived as a function of p T and η of the jet, as well as of the pileup conditions and the jet flavor composition of the selected jet sample. They are determined using a combination of simulated samples and studies of data, such as measurements of the jet p T balance in dijet, Z+jet and γ+jet events [108]. The systematic uncertainties related to the modeling of E miss T in the simulation are estimated by propagating the uncertainties in the energy and momentum scale of each of the objects entering the calculation, as well as the uncertainties in the soft-term resolution and scale [113].
The reconstruction, identification and isolation efficiencies for low-p T leptons, as well as the momentum resolution and scale, are measured and calibrated following methods similar to those employed for higher-p T electrons [103] and muons [102]. The associated systematic uncertainties are in general found to be small.
The MC samples simulating the dominant background processes, tt/tW, Z ( * ) /γ * (→ ττ) + jets and VV, are also affected by different sources of theoretical modeling uncertainty. The uncertainties related to the choice of QCD renormalization and factorization scales are assessed by varying the corresponding generator parameters up and down by a factor of two around their nominal values. Uncertainties in the resummation scale and the matching scale between matrix elements and parton showers for the Z ( * ) /γ * (→ ττ) + jets samples are evaluated by varying up and down by a factor of two the corresponding parameters in S . The uncertainties associated with the choice of PDF set, NNPDF [54,84], and uncertainty in the strong coupling constant, α s , are also considered.
As discussed in Section 6, the background predictions in the 1 1T SR, selecting OS lepton-track pairs, are extracted from a SS data control sample. Two different types of systematic uncertainty are associated with the OS-SS extrapolation. For m track < 2 GeV, low-mass resonances can cause higher production rates for OS events than for SS events. A 30% uncertainty is assigned, based on an exponential fit to the OS/SS ratio as a function of E miss T in the ∆φ(lep, p miss T ) > 1.5 region. This OS/SS ratio was found to be constant and equal to 1 for E miss T > 200 GeV, indicating low-mass resonances do not contribute significantly to the OS sample in the SR-E-1 1T region. The uncertainty is computed as the value of the fitting function at E miss T = 200 GeV, where the deviation from unity is largest, summed linearly with the corresponding fit uncertainty. The m track > 2 GeV region is instead mainly populated by W+jets events, in which the correlation between the lepton and the track charge may introduce differences between the SS and OS expectations. A 12% uncertainty, extracted from W+jets simulated events, is assigned.
The m track > 2 GeV region is instead mainly populated by W+jets events, in which the correlation between the lepton and the track charge may introduce differences between the SS and OS expectations. A 12% uncertainty, extracted from W+jets simulated events, is assigned.
Uncertainties in the expected yields for non-VBF SUSY samples arising from generator modeling are determined in situ by comparing the yields from Z → µµ events in data with those from Z(→ µµ)+jets    events generated using the same MG5_aMC@NLO configuration as the signal samples. The muon fourmomenta are added to the E miss T to emulate the p T of the SUSY system in signal events, and uncertainties are derived from observed differences in E miss T between data and simulation. The largest modeling uncertainties are approximately 20% for samples with the most compressed mass spectrum and in high-E miss T channels, while low-E miss T channels and noncompressed signal points have uncertainties ranging from 1% to 10%. Uncertainties in the signal acceptance due to PDF uncertainties are evaluated following the PDF4LHC15 recommendations [121] and amount to at most 15% for large χ 0 2 or masses. Uncertainties in the shape of the m or m 100 T2 signal distributions due to the sources above are found to be small, and are neglected. Uncertainties due to generator modeling in the acceptance of the VBF signal samples are evaluated by varying by a factor of two the MG5_aMC@NLO parameters corresponding to the renormalization, factorization and CKKW-L matching scales, as well as the P 8 shower tune parameters and α s . The largest uncertainties arise from renormalization and factorization scale variations (13%-22%), with smaller contributions from matching and α s variations (0.5%-5%).
Additional uncertainties are assigned to the predictions from signal simulation in the 1 1T SR. An uncertainty in the modeling of the rate for reconstructed tracks that do not match a generated charged particle is accounted for. It is estimated by comparing the nonlinear component of the per-event track multiplicity as a function of pileup, in data and simulation. Furthermore, the calibration procedure applied to MC events to match the track impact parameter resolution in different data-taking periods is also a source of systematic uncertainty. Finally, uncertainties are assigned to the track-lepton matching efficiency and the track isolation efficiency, as derived from the studies of events with a J/ψ meson or Z boson decaying into a lepton and a track, described in Section 4.

Results
Data in the control regions, validation regions, and signal regions are compared with SM predictions using a profile likelihood method [122] implemented in the H F package [123]. Most systematic uncertainties are treated as nuisance parameters with Gaussian constraints in the likelihood, apart from those of statistical nature, for which Poisson constraints are used. Experimental systematic uncertainties are correlated between signal and backgrounds for all regions.

Control and validation regions
A background-only fit of the CRs is constructed using only the control regions to constrain the fit parameters. The data in the control regions CRtop, CRtau and CRVV are fit simultaneously in each search to constrain overall normalization factors for the tt/Wt, Z ( * ) /γ * (→ ττ) + jets, and VV background predictions. The resulting normalization parameters are presented in Table 9.
The background prediction as obtained from the background-only fit of the CRs is then compared with data in the validation regions to verify the accuracy of the background modeling. Figure 6 shows a comparison of the data yields with background predictions in the VRDF regions, binned in m and m 100 T2 using the same intervals as defined for the corresponding SRs. Good agreement is observed in all event selection categories, with deviations below 2σ. Examples of kinematic distributions in control and validation regions are presented in Figures 7 through 9, where good agreement between data and MC simulation is seen in both the shape and normalization of the discriminating variables.

Inclusive signal regions
The inclusive signal regions defined in Section 5 are used to test for excesses of events above the SM predictions. Each fit only considers one single-bin inclusive signal region, and includes a signal model with an unconstrained normalization parameter to estimate the contributions of any phenomena beyond those predicted by the Standard Model. The signal region is fit simultaneously with the control regions, which are assumed to contain no signal, resulting in background estimates constrained by the background-only fit of the CRs.
To quantify the probability under the background-only hypothesis to produce event yields greater than or equal to the observed data, the discovery p-values are calculated for each inclusive signal region. The results for the electroweakino, VBF, and slepton regions are shown in Table 10. Several electroweakino regions have low p-values, with the lowest observed in the m < 20 GeV bin corresponding to a local significance of 2.7σ. The CL s prescription [124] is used to perform a hypothesis test that sets upper limits at the 95% confidence level (CL) on the observed (expected) number of signal events S 95 obs (exp) in each inclusive signal region. Dividing S 95 obs by the integrated luminosity defines the upper limits on the visible cross-sections σ 95 obs . Table 10: Left to right: The first column indicates the inclusive signal region under study, defined as the union of the individual SRs defined in Section 5 and by upper bounds on m or m 100 T2 in GeV. The m regions include events in both the 2 and 1 1T channels, while the m 100 T2 regions only include 2 events. The next two columns present observed (N obs ) and expected (N exp ) event yields in the inclusive signal regions. The latter are obtained by the background-only fit of the CRs, and the errors include both the statistical and systematic uncertainties. The next two columns show the observed 95% CL upper limits on the visible cross-section σ 95 obs and on the number of signal events S 95 obs . The next column S 95 exp shows the 95% CL upper limit on the number of signal events, given the expected number (and ±1σ deviations from the expectation) of background events. The last column indicates the discovery p-value (p(s = 0)).

Exclusive signal regions and model-dependent interpretations
The exclusive signal regions are used to constrain specific SUSY models. An exclusion fit extends a background-only fit of the CRs to include signal regions relevant for the model under study. All regions are fit simultaneously with a parameter of interest corresponding to the signal strength, a factor that coherently scales the signal yield across all regions. In order to assess the stability of the exclusion fit, a "CR+SR background-only fit" of the CRs and the exclusive signal regions is performed in which the signal strength is fixed to zero. Comparisons of the data yields with background prediction in the m and m 100 T2 bins of the SRs, after the CR+SR background-only fit, are shown in Tables 11-14 and Figure 10, with all deviations less than 2σ. Examples of kinematic distributions in the SRs after a background-only fit of the CRs are presented in Figures 11, 12 and 13, where good agreement between data and the background predictions is seen in both the shape and the normalization of the discriminating variables. Table 11: Observed event yields and fit results using a CR+SR background-only fit for the exclusive electroweakino signal regions. Background processes containing fewer than two prompt leptons are categorized as 'Fake/nonprompt'. The category 'Others' contains rare backgrounds from triboson, Higgs boson, and the remaining top-quark production processes listed in Table 1  Fitted SM events 0.5 ± 0.5 6.0 ± 1.9 7.6 ± 2.1 20.7 ± 3.4 24 ± 4 18.1 ± 3.1 Table 13: Observed event yields and fit results using a CR+SR background-only fit for the exclusive VBF signal regions. Background processes containing fewer than two prompt leptons are categorized as 'Fake/nonprompt'. The category 'Others' contains rare backgrounds from triboson, Higgs boson, and the remaining top-quark production processes listed in Table 1. Uncertainties in the fitted background estimates combine statistical and systematic uncertainties.
SR-E-med      The CL s prescription is used to perform hypothesis tests of specific SUSY models. The SRs defined using m are used for electroweakino models, while regions defined using m 100 T2 are used for slepton models. Exclusions at 95% confidence level are presented in a two-dimensional plane with the horizontal axis given by the mass of the χ 0 2 , and the vertical axis defined by the difference in mass between the χ 0 2 or slepton and the χ 0 1 . Exclusion contours for both wino and higgsino production are shown in Figure 14. Most of the exclusion power originates from the high-E miss T channel, with added sensitivity provided by the 1 1T search at small mass splittings and by the low-E miss T channels at higher mass splittings. The behavior of the observed exclusion contours at large ∆m( χ 0 2 , χ 0 1 ) is due to the SM background expectation underestimating the data for events with 10 < m µµ < 20 GeV in SR-E-high, while it overestimates for events with 20 < m µµ < 40 GeV in the same signal region. This is also visible in Figure 10, which shows the results of a CR+SR background-only fit assuming that no signal is present. The lack of allowed contributions from signal processes in the SR-constrained fit reduces the significance of bin-by-bin deviations, while the presence of a signal normalization parameter in the exclusion fit allows for larger deviations from the background constraints. When assuming wino production with m( χ 0 2 ) × m( χ 0 1 ) > 0, electroweakino masses of up to 240 GeV for mass splittings of 7 GeV are excluded. For electroweakino masses at the edge of LEP exclusions, mass splittings from 1.5 GeV to 46 GeV are excluded. Assuming higgsino production, χ 0 2 masses below 193 GeV are excluded for mass splittings of 9.3 GeV. At the LEP bounds on m( χ 0 2 ), mass splittings from 2.4 GeV to 55 GeV are excluded. All observed limits are within 2σ of the median expected limit.
Models containing electroweakinos produced through VBF processes are constrained using the VBF signal regions. These constraints are shown in Figure 15. The limits on VBF higgsino production cross-sections have a weak dependence on the mass splittings and are shown assuming ∆m = 5 GeV. Higgsinos with masses below 55 GeV are excluded for mass splittings of 5 GeV. Assuming VBF production of winos, electroweakino masses up to 76 GeV for mass splittings of 4.5 GeV are excluded. For wino masses near half of the Higgs boson mass, mass splittings between 2 GeV and 32 GeV are excluded.
Exclusion contours for light-flavor sleptons are shown in Figure 16. Assuming mass-degenerate selectrons and smuons, slepton masses below 251 GeV are excluded for mass splittings of 10 GeV. For sleptons with masses just above the LEP limits, mass splittings from 550 MeV to 30 GeV are excluded. Figure 16 also shows results where only the right/left-handed selectron or smuon is produced. When producing these results, only ee or µµ events in the SRs are considered. Right-handed sleptons have smaller cross-sections than their left-handed counterparts, due to their different couplings to the weak gauge fields    Figure 14: Expected 95% CL exclusion sensitivity (blue dashed line), with ±1σ exp (yellow band) from experimental systematic uncertainties and statistical uncertainties on the data yields, and observed limits (red solid line) with ±1σ theory (dotted red line) from signal cross-section uncertainties for simplified models of direct higgsino (top) and wino (bottom) production. A fit of signals to the m spectrum is used to derive the limit, which is projected into the ∆m( χ 0 2 , χ 0 1 ) vs. m( χ 0 2 ) plane. For higgsino production, the chargino χ ± 1 mass is assumed to be halfway between the χ 0 2 and χ 0 1 masses, while m( χ 0 2 ) = m( χ ± 1 ) is assumed for the wino/bino model. Following the discussion in Section 3, the m shape in the wino/bino model depends on the relative sign of the χ 0 1 and χ 0 2 mass parameters. The bottom left plot assumes m( χ 0 1 ) × m( χ 0 2 ) < 0, while m( χ 0 1 ) × m( χ 0 2 ) > 0 is assumed on the bottom right. The gray regions denote the lower chargino mass limit from LEP [30] Figure 15: Expected 95% CL exclusion sensitivity (blue dashed line) and observed limits (red solid line) for simplified models of higgsino (left) and wino (right) production through VBF. A fit of signals to the m spectrum in the VBF signal regions is used to derive the limit. On the left, the limit for higgsinos is shown as a function of m( χ 0 2 ) for a mass splitting of ∆m( χ 0 2 , χ 0 1 ) = 5 GeV (the chargino χ ± 1 mass is assumed to be halfway between the χ 0 2 and χ 0 1 masses). The yellow band indicates ±1σ exp from experimental systematic uncertainties and statistical uncertainties on the data yields. On the right the limit for winos is projected into the ∆m( χ 0 2 , χ 0 1 ) vs. m( χ 0 2 ) plane (m( χ 0 2 ) = m( χ ± 1 ) is assumed for the wino/bino model). The red dotted line indicates the ±1σ theory from signal cross-section uncertainties and the colored map illustrates the 95% CL upper limits on the cross-section. The cross-section corresponds to the leading-order prediction from MG5_aMC@NLO for the process pp → χ 0 2 χ ± 1 j j including the parton-level requirements described in Section 3. The contour lines represent steps of 0.2 pb. Expected limit (μL) Observed limit (μL) Expected limit (μR) Observed limit (μR) Expected limit (ẽL) Observed limit (ẽL) Expected limit ( Figure 16: Expected 95% CL sensitivity (dashed lines) and observed limits (solid lines) for simplified models of direct slepton production. A fit of slepton signals to the m 100 T2 spectrum is used to derive the limits, which are projected into the ∆m( , χ 0 1 ) vs. m( ) plane. Slepton refers to the scalar partners of left-and right-handed electrons and muons. The gray region is the e R limit from LEP [30]. On the left, the sleptons are assumed to be fourfold mass degenerate with m( e L ) = m( e R ) = m( µ L ) = m( µ R ), the expected sensitivity (blue dashed line) is shown with with ±1σ exp (yellow band) from experimental systematic uncertainties and statistical uncertainties on the data yields, the observed limit (red solid line) is shown with ±1σ theory (dotted red line) from signal cross-section uncertainties, and the blue regions are the fourfold mass-degenerate slepton limits from ATLAS Run 1 [125] and Run 2 [45]. On the right, no degeneracy is assumed for the masses of the sleptons and the limits are presented separately for e L , e R , µ L and µ R .

Conclusion
Results of searches for electroweak production of supersymmetric particles in models with compressed mass spectra are presented, using √ s = 13 TeV proton-proton collision data corresponding to 139 fb −1 collected by the ATLAS experiment at the CERN Large Hadron Collider. Events with missing transverse momentum, two same-flavor, opposite-charge, low transverse momentum leptons, and hadronic activity from initial-state radiation or characteristic of vector-boson fusion production are selected. The data are found to be consistent with predictions from the Standard Model. Assuming wino production, constraints at 95% confidence level are placed on the minimum mass of the χ 0 2 at 240 GeV for a mass splitting of 7 GeV, and extend down to a mass splitting of 1.5 GeV at the LEP chargino mass limit of 92.4 GeV. For higgsino production, the corresponding lower limits are at 193 GeV at a mass splitting of 9.3 GeV, and extend down to a mass splitting of 2.4 GeV at the LEP chargino mass limit. Events consistent with the production of electroweak SUSY states through vector-boson fusion processes are used to constrain wino/bino and higgsino models while assuming a vanishing qq fusion production cross-section. Light-flavor sleptons are constrained to have masses above 251 GeV for a mass splitting of 10 GeV, with constraints extending down to mass splittings of 550 MeV at the LEP slepton limits (73 GeV      [94] N. Kidonakis, Next-to-next-to-leading-order collinear and soft gluon corrections for t-channel single top quark production, Phys. Rev. D 83 (2011)