Search for the electroweak production of supersymmetric particles in $\sqrt{s}$=8 TeV $pp$ collisions with the ATLAS detector

The ATLAS experiment has performed extensive searches for the electroweak production of charginos, neutralinos and staus. This article summarizes and extends the search for electroweak supersymmetry with new analyses targeting scenarios not covered by previously published searches. New searches use vector-boson fusion production, initial-state radiation jets, and low-momentum lepton final states, as well as multivariate analysis techniques to improve the sensitivity to scenarios with small mass splittings and low-production cross-sections. Results are based on 20 fb$^{-1}$ of proton-proton collision data at $\sqrt{s}$=8 TeV recorded with the ATLAS experiment at the Large Hadron Collider. No significant excess beyond Standard Model expectations is observed. The new and existing searches are combined and interpreted in terms of 95% confidence-level exclusion limits in simplified models, where a single production process and decay mode is assumed, as well as within phenomenological supersymmetric models.

The charginos and neutralinos are mixtures of the bino, winos and higgsinos, collectively referred to as the electroweakinos, that are superpartners of the U(1), SU(2) gauge bosons and the Higgs bosons, respectively. Their mass eigenstates are referred to asχ ± i (i = 1, 2) andχ 0 j ( j = 1, 2, 3, 4) in order of increasing mass. The direct production of charginos, neutralinos and sleptons (l) through electroweak (EW) interactions may dominate the SUSY production at the Large Hadron Collider (LHC) if the masses of the gluinos and squarks are large. Previous searches for electroweak SUSY production at ATLAS targeted the production ofl +l− ,τ +τ− ,χ  [19][20][21][22][23], and found no significant excess beyond SM expectations. These searches are typically sensitive to scenarios where there is a relatively large O(m W,Z ) splitting between the produced sparticles and the LSP, leaving uncovered territory for smaller mass splittings.
This article addresses EW SUSY production based on the 20.3 fb −1 of √ s = 8 TeV proton-proton collisions collected by the ATLAS experiment in 2012. A series of new analyses targeting regions in parameter space not covered by previous ATLAS analyses [19][20][21][22][23] are presented. The results from new and published searches are combined and reinterpreted to provide the final 8 TeV ATLAS limits on the production of EW SUSY particles in a variety of models. The dependence of the limits on the mass of the intermediate slepton in models of electroweakino production withl-mediated decays is also studied, thus generalizing the results of Refs. [19][20][21].
In cases where the LSP is wino-or higgsino-dominated, the lighter electroweakino statesχ ± 1 ,χ 0 2 can have mass differences with theχ 0 1 ranging from a few MeV to a few tens of GeV, depending on the values of the other parameters in the mixing matrix [24]. In particular, in naturalness-inspired models [25,26] the higgsino must be light, so theχ 0 1 ,χ 0 2 andχ ± 1 are usually higgsino-dominated and have a small mass splitting. Therefore, a situation with a lightχ 0 1 approximately mass degenerate with theχ ± 1 andχ 0 2 has a strong theoretical motivation. A relatively low mass splitting between the produced sparticles and the LSP (referred to as compressed scenarios) results in low-momentum decay products that are difficult to reconstruct efficiently, and probing these signatures is experimentally challenging. The new analyses introduced in this article improve the sensitivity to the compressed spectra. The two-and three-lepton searches forχ + 1χ − 1 andχ ± 1χ 0 2 production in Refs. [19,20] are extended by lowering the transverse momentum threshold on reconstructed leptons, and by boosting the electroweak SUSY system through the requirement of QCD initial state radiation (ISR). The search for the vector-boson fusion (VBF) production ofχ ± 1χ ± 1 uses the signature of a same-sign light lepton (e, µ) pair with two jets to probe compressed spectra.
In many SUSY scenarios with large tan β, the stau (τ) is lighter than the selectron and smuon [27], resulting in tau-rich final states. Co-annihilation processes [28] favor a lightτ that has a small mass splitting with a bino LSP, as it can set the relic density to the observed value [29]. An additional new search is presented here, which uses a final state with two hadronically decaying τ leptons and multivariate techniques to improve the sensitivity to directτ production compared to the search presented in Ref. [22].
The article is organized as follows: Section 2 describes the signal models studied in this article; Section 3 provides a brief description of the ATLAS detector; Sections 4 and 5 outline the Monte Carlo (MC) simulation and event selection, respectively; Section 6 discusses the analysis strategy common to all analyses studied in this article; Section 7 presents the direct stau production search; Section 8 presents the compressed spectra searches in direct production; Section 9 presents the search for same-sign charginopair production via VBF; Section 10 provides a global overview of the results of the ATLAS searches for electroweakino production at 8 TeV, integrating the results of the new analyses with published analyses in the framework of several relevant signal models; finally conclusions are drawn in Section 11.

SUSY scenarios
The SUSY scenarios considered in this article can be divided into two categories: simplified models and phenomenological models. The simplified models [40] target the production of charginos, neutralinos and sleptons, where the masses and the decay modes of the relevant particles are the only free parameters. In each of the simplified models, a single production process with a fixed decay chain is considered for optimization of the event selection and interpretation of the results. To illustrate the range of applicability of the searches, several classes of phenomenological models that consider all relevant SUSY production and decay processes are also used to interpret the results. These models include the five-dimensional EW phenomenological Minimal Supersymmetric Standard Model (pMSSM) [41], the Non Universal Higgs Masses (NUHM) model [42,43], and a Gauge-Mediated SUSY Breaking (GMSB) model [44][45][46][47][48][49].
R-parity is assumed to be conserved in all SUSY scenarios considered in this article. The LSP is assumed to be the lightest neutralinoχ 0 1 except in the GMSB scenarios, where it is the gravitinoG. The next-to-LSP (NLSP) is usually one or more of the charginos, neutralinos or sleptons. All SUSY particles are assumed to decay promptly, with the exception of the LSP, which is stable. Finally, SUSY particles that are not considered in a given model are decoupled by setting their masses to values inaccessible at the LHC.
Unless stated otherwise, signal cross-sections are calculated to next-to-leading order (NLO) in the strong coupling constant using Prospino2 [50], and are shown in Figure 1 for a number of selected simplifiedmodel production modes. The cross-sections for the production of charginos and neutralinos are in agreement with the NLO calculations matched to resummation at next-to-leading logarithmic accuracy (NLO+NLL) within about two percent [51][52][53]. The nominal cross-section and the uncertainty are taken from the center and spread, respectively, of the envelope of cross-section predictions using different parton distribution function (PDF) sets and factorization and renormalization scales, as described in Ref. [54].

Direct stau-pair production simplified model
Two simplified models describing the direct production ofτ +τ− are used in this article: one considers stau partners of the left-handed τ lepton (τ L ), and a second considers stau partners of the right-handed τ lepton (τ R ). In both models, the stau decays with a branching fraction of 100% to the SM tau-lepton and the LSP. The diagram for this model can be seen in Figure 2(a).
In the simplified models considered here, the slepton mass is assumed to lie between theχ 0 1 andχ ± 1 /χ 0 2 masses, which increases the branching fraction to leptonic final states compared to scenarios without sleptons.
The compressed spectra searches in this article are less sensitive to scenarios where theχ ± 1 /χ 0 2 decay through SM W, Z or Higgs bosons, as the branching fraction to leptonic final states is significantly suppressed. The results of the ATLAS searches forχ + 1χ − 1 production with WW-mediated decays [19],χ ± 1χ 0 2 production with WZ-mediated decays [20] andχ ± 1χ 0 2 production with Wh-mediated decays [23] are summarized in Section 10.5. In these scenarios with decays mediated by SM bosons, the W, Z and h bosons are assumed to decay with SM branching fractions.
In the simplified models of the direct production ofχ

Simplified model of same-sign chargino-pair production via vector-boson fusion
A simplified model forχ ± 1χ ± 1 production via VBF [55,56] is also considered. As in the case of direct production, theχ ± 1 is assumed to be pure wino, and mass-degenerate with theχ 0 2 , and theχ 0 1 is assumed to be pure bino. Theχ ± 1 decays with a branching fraction of 1/6 viaẽ L ,μ L ,τ L ,ν e ,ν µ , orν τ with masses mν ℓ = ml L = 0.5(mχ± 1 + mχ0 1 ). The diagram forχ ± 1χ ± 1 production via VBF, where the sparticles are produced along with two jets, is shown in Figure 2(e). The jets are widely separated in pseudorapidity 1 η and have a relatively high dijet invariant mass m j j . Due to the VBF topology, the charginos are often boosted in the transverse plane, forcing the decay products to be more collinear and energetic, even in highly compressed spectra. This feature of VBF production makes it a good candidate to probe compressed SUSY scenarios that are experimentally difficult to explore via the direct production modes. The signal cross-sections are calculated to leading order (LO) in the strong coupling constant using MadGraph 5-1.3.33 [57] (more details on the cross-section calculation are given in Appendix A). The uncertainties on the signal cross-sections are calculated by using different PDF sets (2%) and by varying the renormalization and factorization scales between 0.5 and 2 times the nominal values (6%) [58]. For aχ ± 1 with mass of 120 GeV, the cross-section forχ ± 1χ ± 1 production in association with two jets satisfying the criteria m j j > 350 GeV and |∆η j j | > 1.6 is 1.1 fb. For the assumed mixings in the chargino-neutralino sector, and the mass values considered in the analysis, the cross-section forχ ± 1χ ± 1 VBF production is found to be independent of theχ 0 1 mass. 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 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 upward. 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).

Phenomenological Minimal Supersymmetric Standard Model
The analysis results are interpreted in a pMSSM scenario. The masses of the sfermions, the gluino, and of the CP-odd Higgs boson are set to high values (2 TeV, 2 TeV and 500 GeV respectively), thus decoupling the production of these particles and allowing only the direct production of charginos and neutralinos decaying via SM gauge bosons and the lightest Higgs boson. The remaining four parameters, the ratio of the expectation values of the two Higgs doublets (tan β), the gaugino mass parameters M 1 and M 2 , and the higgsino mass parameter µ, determine the phenomenology of direct electroweak SUSY production. For the analysis presented here, µ and M 2 are treated as free parameters. The remaining parameters are fixed to tan β = 10 and M 1 = 50 GeV, so that the relic dark-matter density is below the cosmological bound [29] across most of the µ-M 2 grid. The lightest Higgs boson has a mass close to 125 GeV, which is set by tuning the mixing in the top squark sector, and decays to SUSY as well as SM particles where kinematically allowed.

Two-parameter Non Universal Higgs Masses model
Radiatively-driven natural SUSY [59] allows the Z and Higgs boson masses to be close to 100 GeV, with gluino and squark masses beyond the TeV scale. In the two-parameter NUHM model (NUHM2) that is considered in this article, the direct production of charginos and neutralinos is dominant in a large area of the parameter space considered. The mass hierarchy, composition and production cross-section of the SUSY particles are governed by the universal soft SUSY-breaking scalar mass m 0 , the soft SUSYbreaking gaugino mass m 1/2 , the trilinear SUSY-breaking parameter A 0 , the pseudoscalar Higgs boson mass m A , tan β and µ. Both µ and m 1/2 are treated as free parameters and the other parameters are fixed to m 0 = 5 TeV, A 0 = −1.6 m 0 , tan β = 15, m A = 1 TeV, and sign(µ) > 0. These conditions ensure a low level of electroweak fine tuning, while keeping the lightest Higgs boson mass close to 125 GeV and the squark masses to a few TeV. The gluino mass typically satisfies mg ≃ 2.5m 1/2 . For low gluino masses, the production of strongly interacting SUSY particles dominates; as the gluino mass increases the production of electroweakinos becomes more important. The charginos and neutralinos decay via W, Z and Higgs bosons.

Gauge-Mediated SUSY Breaking model
Minimal GMSB models are described by six parameters: the SUSY-breaking mass scale in the low-energy sector (Λ), the messenger mass (M mess ), the number of SU(5) messenger fields (N 5 ), the scale factor for the gravitino mass (C grav ), tan β, and µ. In the model presented here, Λ and tan β are treated as free parameters, and the remaining parameters are fixed to M mess = 250 TeV, N 5 = 3, C grav = 1 and sign(µ) > 0. For high Λ values, the EW production of SUSY particles dominates over other SUSY processes. In most of the relevant parameter space, the NLSP is theτ for large values of tan β (tan β>20), and the final states contain two, three or four tau-leptons. In the region where the mass difference between the stau and selectron/smuon is smaller than the sum of the tau and the electron/muon masses, the stau, selectron and smuon decay directly into the LSP and a lepton, defining the phenomenology. The charginos and neutralinos decay asχ

The ATLAS detector
The ATLAS detector [60] is a multipurpose particle physics detector with forward-backward symmetric cylindrical geometry. The inner tracking detector (ID) covers |η| < 2.5 and consists of a silicon pixel detector, a semiconductor microstrip detector, and a transition radiation tracker. The ID is surrounded by a thin superconducting solenoid providing a 2 T axial magnetic field. A high-granularity lead/liquid-argon sampling calorimeter measures the energy and the position of electromagnetic showers within |η| < 3.2. Sampling calorimeters with liquid argon as the active medium are also used to measure hadronic showers in the endcap (1.5 < |η| < 3.2) and forward (3.1 < |η| < 4.9) regions, while a steel/scintillator tile calorimeter measures hadronic showers in the central region (|η| < 1.7). The muon spectrometer (MS) surrounds the calorimeters and consists of three large superconducting air-core toroid magnets, each with eight coils, a system of precision tracking chambers (|η| < 2.7), and fast trigger chambers (|η| < 2.4). A three-level trigger system [61] selects events to be recorded for offline analysis.

Monte Carlo simulation
Monte Carlo (MC) generators are used to simulate SM processes and new physics signals. The SM processes considered are those that can lead to leptonic signatures. Details of the signal and background MC simulation samples used in this article, as well as the order of cross-section calculations in perturbative QCD used for yield normalization are shown in Table 1.
For all MC simulation samples, the propagation of particles through the ATLAS detector is modeled with Geant 4 [96] using the full ATLAS detector simulation [97], or a fast simulation using a parametric response of the electromagnetic and hadronic calorimeters [98] and Geant 4 elsewhere. The effect of multiple proton-proton collisions in the same or nearby beam bunch crossings (in-time and out-of-time pileup) is incorporated into the simulation by overlaying additional minimum-bias events generated with Pythia-8 onto hard-scatter events. Simulated events are weighted to match the distribution of the mean number of interactions per bunch crossing in data, and are reconstructed in the same manner as data. The simulated MC samples are corrected to account for differences with respect to the data in the heavy-flavor quark jet selection efficiencies and misidentification probabilities, lepton efficiencies, tau misidentification probabilities, as well as the energy and momentum measurements of leptons and jets. Theχ 0 2 ) signal samples simulated with Herwig++ are reweighted to match theχ 2 ) system transverse momentum distribution obtained from the MadGraph samples that are generated with an additional parton in the matrix element to give a better description of the ISR.

Event reconstruction
Events recorded during stable data-taking conditions are analyzed if the reconstructed primary vertex has five or more tracks with transverse momentum p T > 400 MeV associated with it. The primary vertex of an event is identified as the vertex with the highest Σp 2 T of associated tracks. After the application of beam, detector and data-quality requirements, the total luminosity considered in these analyses corresponds to 20.3 fb −1 (20.1 fb −1 for the direct stau production analysis due to a different trigger requirement).
Electron candidates are required to have |η| < 2.47 and p T > 7 GeV, where the p T and η are determined from the calibrated clustered energy deposits in the electromagnetic calorimeter and the matched ID track, respectively. Electrons must satisfy "medium" identification criteria, following Ref. [99]. Muon candidates are reconstructed by combining tracks in the ID and tracks in the MS [100], and are required to have |η| < 2.5 and p T > 5 GeV. Events containing one or more muons that have transverse impact parameter with respect to the primary vertex |d 0 | > 0.2 mm or longitudinal impact parameter with respect to the primary vertex |z 0 | > 1 mm are rejected to suppress cosmic-ray muon background. In the direct stau production analysis, and the two-lepton compressed spectra analyses, electrons and muons are required to have p T > 10 GeV.
Jets are reconstructed with the anti-k t algorithm [101] with a radius parameter of R = 0.4. Three-dimensional calorimeter energy clusters are used as input to the jet reconstruction. The clusters are calibrated using the local hadronic calibration [102], which gives different weights to the energy deposits from the electromagnetic and hadronic components of the showers. The final jet energy calibration corrects the calorimeter response to the particle-level jet energy [102,103], where correction factors are obtained from simulation and then refined and validated using data. Corrections for in-time and out-of-time pileup are also applied based on the jet area method [102]. Central jets must have |η| < 2.4 and p T > 20 GeV, and a "jet vertex fraction" [102] (JVF) larger than 0.5 if p T < 50 GeV. The JVF is the p T -weighted fraction of the tracks in the jet that are associated with the primary vertex. Requiring large JVF values suppresses jets from pileup. Forward jets are those with 2.4 < |η| < 4.5 and p T > 30 GeV. Events containing jets failing to satisfy the quality criteria described in Ref. [102] are rejected to suppress events with large calorimeter noise and noncollision backgrounds.
Central jets are identified as containing b-hadrons (referred to as b-tagged) using a multivariate technique based on quantities related to reconstructed secondary vertices. The chosen working point of the b-tagging algorithm [104] correctly identifies b-hadrons in simulated tt samples with an efficiency of 80%, with a light-flavor jet misidentification probability of about 4% and a c-jet misidentification probability of about 30%.
Hadronically decaying τ leptons (τ had ) are reconstructed using jets described above with |η| < 2.47 and a lower p T threshold of 10 GeV. The τ had reconstruction algorithm uses information about the tracks within ∆R ≡ (∆φ) 2 + (∆η) 2 = 0.2 of the seed jet, in addition to the electromagnetic and hadronic shower shapes in the calorimeters. The τ had candidates are required to have one or three associated tracks (prongs), as τ leptons predominantly decay to either one or three charged pions together with a neutrino and often additional neutral pions. The τ had candidates are required to have p T > 20 GeV and unit total charge of their constituent tracks. A boosted decision tree algorithm (BDT) uses discriminating track and cluster variables to optimize τ had identification, where "loose", "medium" and "tight" working points are defined [105]. Electrons misidentified as τ had candidates are vetoed using transition radiation and calorimeter information. The τ had candidates are corrected to the τ energy scale [105] using an ηand p T -dependent calibration. Kinematic variables built using taus in this article use only the visible decay products from the hadronically decaying tau.
The missing transverse momentum is the negative vector sum of the transverse momenta of all muons with p T > 10 GeV, electrons with p T > 10 GeV, photons with p T > 10 GeV [99], jets with p T > 20 GeV, and calibrated calorimeter energy clusters with |η| < 4.9 not associated with these objects. Hadronically decaying τ leptons are included in the E miss T calculation as jets. Clusters associated with electrons, photons and jets are calibrated to the scale of the corresponding objects. Calorimeter energy clusters not associated with these objects are calibrated using both calorimeter and tracker information [106]. For jets, the calibration includes the pileup correction described above, whilst the JVF requirement is not considered when selecting jet candidates.
To avoid potential ambiguities among objects, "tagged" leptons are candidate leptons separated from each other and from jets in the following order: 1. If two electron candidates are reconstructed with ∆R < 0.1, the lower energy candidate is discarded. 2. Jets within ∆R = 0.2 of an electron candidate, and τ had candidates within ∆R = 0.2 of an electron or muon, are discarded. 3. Electron and muon candidates are discarded if found within ∆R = 0.4 of a remaining jet to suppress leptons from semileptonic decays of c-and b-hadrons. 4. To reject bremsstrahlung from muons, eµ (µµ) pairs are discarded if the two leptons are within ∆R = 0.01 (0.05) of one another. 5. jets found within ∆R = 0.2 of a "signal" τ lepton (see below) are discarded.
Finally, to suppress low-mass decays, if tagged electrons and muons form a same-flavor opposite-sign (SFOS) pair with m SFOS < 2 GeV, both leptons in the pair are discarded.
Tagged leptons satisfying additional identification criteria are called "signal" leptons. To maximize the search sensitivity, some analyses presented in this article require different additional criteria for signal leptons and these are highlighted where necessary. Signal τ leptons must satisfy "medium" identification criteria [105], while for the final signal-region selections, both the "medium" and "tight" criteria are used. Unless stated otherwise, signal electrons (muons) are tagged electrons (muons) for which the scalar sum of the transverse momenta of tracks within a cone of ∆R = 0.3 around the lepton candidate is less than 16% (12%) of the lepton p T . Tracks used for the electron (muon) isolation requirement defined above are those that have p T > 0.4 (1.0) GeV and |z 0 | < 2 mm with respect to the primary vertex of the event. Tracks of the leptons themselves as well as tracks closer in z 0 to another vertex (that is not the primary vertex) are not included. The isolation requirements are imposed to reduce the contributions from semileptonic decays of hadrons and jets misidentified as leptons. Signal electrons must also satisfy "tight" identification criteria [99] and the sum of the extra transverse energy deposits in the calorimeter (corrected for pileup effects) within a cone of ∆R = 0.3 around the electron candidate must be less than 18% of the electron p T . To further suppress electrons and muons originating from secondary vertices, the d 0 normalized to its uncertainty is required to be small, with |d 0 |/σ(d 0 ) < 5 (3), and |z 0 sin θ| < 0.4 mm (1 mm) for electrons (muons).

General analysis strategy
The broad range of EW SUSY scenarios considered by the ATLAS experiment is accompanied by a large number of experimental signatures: from the two-tau signature from direct stau production, to threelepton signatures fromχ ± 1χ 0 2 production. As much as possible the individual analyses follow a common approach. Signal regions (SR) are defined to target one or more EW SUSY scenarios, using kinematic variables with good signal-background separation, as described in Section 6.1. The optimization of key selection variables is performed by maximizing the expected sensitivity to the signal model. A common background estimation strategy is used for the analyses in this article: the main SM backgrounds are estimated by normalizing MC simulation samples to data in dedicated control regions (CRs); backgrounds due to non-prompt and fake leptons are derived from data as outlined in Section 6.2, while small backgrounds are estimated purely using MC simulation samples. The HistFitter [107] software framework is used in all analyses for constraining the background normalizations and the statistical interpretation of the results.
The CRs are defined with kinematic properties similar to the SRs, yet are disjoint from the SR, and have high purity for the background process under consideration. The CRs are designed in a way that minimizes the contamination from the signal model and cross-contamination between multiple CRs is taken into account in the normalization to data. To validate the modeling of the SM backgrounds, the yields and shapes of key kinematic variables are compared to data in validation regions (VR). The VRs are defined to be close to, yet disjoint from the SR and CR, and be dominated by the background process under consideration. The VRs are designed such that the contamination from the signal model is low. Three different fit configurations are used. The "background-only fit" is used for estimating the expected background in the SRs and VRs using observations in the CRs, with no assumptions made on any signal model. In the absence of an observed excess of events in one or more signal regions, the "model-dependent signal fit" is used to set exclusion limits in a particular model, where the signal contribution from the particular model that is being tested is taken into account in all CR and SR. Finally, in the "model-independent signal fit", both the CRs and SRs are used in the same manner as for the model-dependent signal fit, but signal contamination is not accounted for in the CRs. A likelihood function is built as the product of Poisson probability functions, describing the observed and expected number of events in the CRs and SRs. The observed number of events in various CRs and SRs are used in a combined profile likelihood fit to determine the expected SM background yields in each of the SRs. The systematic uncertainties on the expected background yields described in Section 6.3 are included as nuisance parameters, constrained to be Gaussian with a width determined by the size of the uncertainty. Correlations between control and signal regions, and background processes, are taken into account with common nuisance parameters. The free parameters and the nuisance parameters are determined by maximizing the product of the Poisson probability functions and the Gaussian constraints on the nuisance parameters.
After the background modeling is understood and validated, the predicted background in the SR is compared to the observed data. In order to quantify the probability for the background-only hypothesis to fluctuate to the observed number of events or higher, the one-sided p 0 -value is calculated. For this calculation, the profile likelihood ratio is used as a test statistic to exclude the signal-plus-background hypothesis if no significant excess is observed. A signal model can be excluded at 95% confidence level (CL) if the CL s [108] of the signal plus background hypothesis is <0.05. For each signal region, the expected and observed upper limits at 95% CL on the number of beyond-the-SM events (S 95 exp and S 95 obs ) are calculated using the model-independent signal fit. The 95% CL upper limits on the signal cross-section times efficiency ( ǫσ 95 obs ) and the CL b value for the background-only hypothesis are also calculated for each analysis in this article. 1 ). Similar to m T2 , M R ∆ is sensitive to the squared mass difference of the pair-produced massive particle and the invisible particle, via a kinematic endpoint. These two variables are expected to provide a similar performance for discriminating the signal from the background. For systems where the invisible particle has a mass that is comparable to the pair-produced massive particle (i.e. compressed spectra), the variable ∆φ β R has a pronounced peak near π. The effect is magnified as the spectrum becomes more and more compressed, making this variable a good discriminator for compressed spectra searches.

Common reducible background estimation
Electron and muon candidates can be classified into three main types, depending on their origin: "real" leptons are prompt and isolated leptons from a W or Z boson, a prompt tau or a SUSY particle decay; "fake" leptons can originate from a misidentified light-flavor quark or gluon jet (referred to as "light flavor"); "non-prompt" leptons can originate from a semileptonic decay of a heavy-flavor quark, from the decay of a meson, or an electron from a photon conversion. The background due to non-prompt and fake electrons and muons, collectively referred to as "reducible", is commonly estimated using the matrix method described in Ref. [112]. The matrix method extracts the number of events with one or two fake or non-prompt leptons from a system of linear equations relating the number of events with two signal or tagged leptons (before signal lepton identification requirements are applied) to the number of events with two candidates that are either real, fake or non-prompt. The coefficients of the linear equations are functions of the real-lepton identification efficiencies and of the fake and non-prompt lepton misidentification probabilities, both defined as a fraction of the corresponding tagged leptons satisfying the signal lepton requirements.
The real-lepton identification efficiencies are obtained from MC simulation samples in the region under consideration to account for detailed kinematic dependencies and are multiplied by correction factors to account for residual differences with respect to the data. The correction factors are obtained from a control region rich in Z → e + e − and Z → µ + µ − decays. The fake and non-prompt lepton misidentification probabilities are calculated as the weighted averages of the corrected type-and process-dependent misidentification probabilities defined below according to their relative contributions in a given signal or validation region. The type-and process-dependent misidentification probabilities for each relevant fake and non-prompt lepton type (heavy-flavor, light-flavor or conversion) and for each reducible background process are corrected using the ratio ("correction factor") of the misidentification probability in data to that in simulation obtained from dedicated control samples. The correction factors are assumed to be independent of the selected regions and of any potential composition or kinematic differences. For non-prompt electrons and muons from heavy-flavor quark decays, the correction factor is measured in a bb-dominated control sample. The correction factor for the conversion candidates is determined in events with a converted photon radiated from a muon in Z → µµ decays.

Common systematic uncertainties
Several sources of systematic uncertainty are considered for the SM background estimates and signal yield predictions. When the MC simulation samples are normalized to data yields in the CR, there is a partial cancellation of both the experimental and theoretical modeling systematic uncertainties.
The experimental systematic uncertainties affecting the simulation-based estimates include: the uncertainties due to the jet energy scale and resolution [100,102]; the uncertainties due to the lepton energy scale, energy resolution and identification efficiency [99,100,105]; the uncertainty due to the hadronic tau misidentification probability [105]; the uncertainty on the E miss T from energy deposits not associated with reconstructed objects (E miss T soft-term resolution) [106]; and the uncertainties due to b-tagging efficiency and mistag probability [104]. The uncertainty on the integrated luminosity is ±2.8% and is derived following the same methodology as that detailed in Ref. [113]. The uncertainty due to the modeling of the pileup in the MC simulation samples is estimated by varying the distribution of the number of interactions per bunch crossing overlaid in the MC samples by ±10%. An uncertainty is applied to MC samples to cover differences in efficiency observed between the trigger in data and the MC trigger simulation.
The systematic uncertainties due to the limitations in theoretical models or calculations affecting the simulation-based background estimates include: the cross-section uncertainties that are estimated by varying the renormalization and factorization scales and the PDFs, and the acceptance uncertainties due to PDFs and the choice of MC generator and parton shower. The cross-section uncertainties for the irreducible backgrounds used here are 30% for ttV [76,77], 50% for tZ, 5% for ZZ, 7% for WZ and 100% for the triboson samples. For the Higgs boson samples, a 20% uncertainty is used for V H and VBF production, while a 100% uncertainty is assigned to ttH and Higgs boson production via gluon fusion [74]. For theχ 0 2 signal simulations that are sensitive to ISR, the impact of the choice of renormalization scales, factorization scales, the scale for the first emission in the so-called MLM matching scheme [114], and MLM matching scale are evaluated by varying these individually between 0.5 and 2 times the nominal values in MadGraph.

Direct stau production
This section presents a search for direct stau-pair production with subsequent decay into final states with two taus and E miss T . The search for direct stau production is very challenging, as the final state is difficult to trigger on and to separate from the SM background. In Ref. [22], the best observed upper limit on the direct stau production cross-section was found for a stau mass of 80 GeV and a masslessχ 0 1 , where the theoretical cross-section at NLO is 0.07 (0.17) pb for right-handed (left-handed) stau-pair production and the excluded cross-section is 0.22 (0.28) pb. This analysis is an update of Ref. [22], using a multivariate analysis technique instead of a simple cut-based method to improve the sensitivity to direct stau-pair production.

Event selection
Events are selected using the basic reconstruction, object and event selection criteria described in Section 5. In addition, if taus form an SFOS pair with m SFOS < 12 GeV, the event is rejected. Events with exactly two hadronically decaying tau candidates are selected, where the two tau candidates are required to have opposite-sign (OS) charge. At least one tau must satisfy the "tight" tau identification BDT requirement and events with additional tagged light leptons are vetoed. Events must satisfy either the single-tau or ditau trigger criteria, as described in Section 5.
To suppress events from Z boson decays, events are rejected if the invariant mass of the tau pair lies within ±10 GeV of the peak value of 81 GeV for Z boson candidates. 2 To suppress background from events containing a top quark, events with b-tagged jets are vetoed. To further select SUSY events from direct stau production and suppress WW and tt production, m T2 is calculated using the two taus and the E miss T in the event. The additional requirement of m T2 > 30 GeV is applied to select events for the training and optimization of the multivariate analysis (MVA).
After applying the preselection listed above, both the signal and background MC samples are split in two. Half is used for the BDT training and the other half for testing. Twelve variables with good discriminatory power are considered as input for the BDT training procedure: ) and ∆φ(E miss T , τ2). The MC simulation samples are compared to data for these variables and their correlations to ensure that they are modeled well.
A direct stau production scenario with m(τ R ,χ 0 1 ) = (109,0) GeV is used for the training and optimization of the BDT, and the BDT response requirement (t cut ) is chosen based on the best expected sensitivity for discovery. The two-tau MVA SR definition is shown in Table 3. Table 3: Two-tau MVA signal region and validation region definitions for the direct stau-pair production analysis, where t cut is the BDT response requirement.
Common exactly 2 medium OS taus

Background determination
The main SM backgrounds in the two-tau MVA SR are W+jets and diboson production. Contributions from diboson, tt, and Z+jets processes are estimated using MC simulation samples and validated using data in WW-rich, tt-rich or Z-rich validation regions, as defined in Ref. [22].
The W+jets contribution in the signal region is dominated by events where the W decays to a tau-lepton and a jet is misidentified as another tau. The contribution is estimated by normalizing the yields from MC simulation samples to data in a dedicated control region. The W+jets control region selects events with the W boson decaying to a muon and neutrino to suppress the multi-jet background, which is larger for the electron channel. Events containing exactly one isolated muon and one tau satisfying the tight identification requirement are selected, where the muon and tau must have opposite electrical charge. To reduce the contribution from Z+jets production, m τ T + m µ T > 80 GeV is required, and the reconstructed invariant mass of the muon and tau must be outside the Z mass window (12 GeV< m τµ < 40 GeV or m τµ > 100 GeV). To further suppress multi-jet and Z+jets processes, E miss T > 40 GeV is required, and the muon and tau must not be back-to-back (∆φ(τ, µ) <2.7 and ∆η(τ, µ) <2.0). The contribution from events with top quarks is suppressed by rejecting events containing b-tagged jets. The multi-jet background in the W+jets control region is estimated using a region with the same requirements, but with a same-sign muon and tau. The contribution from other SM processes is subtracted using MC simulation samples, and the ratio of opposite-sign muon and tau events to same-sign events is assumed to be unity for the multi-jet background.
The contribution from multi-jet events in the signal region, where both selected taus are misidentified jets, is small and is estimated using the so-called ABCD method. Four exclusive regions (A, B, C, D) are defined in a two-dimensional plane as a function of the two uncorrelated discriminating variables m T2 and the tau identification criterion. The regions A and B are required to have two medium taus where at least one meets the tight tau identification criteria, while regions C and D are required to have two loose taus that fail to satisfy the tight tau identification criteria. In regions A and C (B and D) m T2 > 30 GeV (m T2 < 20 GeV) is also required. The multi-jet background in signal region A can be estimated from and N D are the numbers of events in regions A, B, C and D respectively. The assumption that the ratios N A /N C and N B /N D are the same is confirmed using MC simulation samples and in validation regions using data.
A simultaneous likelihood fit to the multi-jet estimation and W+jets CR is performed to normalize the corresponding background estimates and obtain the expected yields in the SR (as described in Section 6). After the simultaneous fit, the multi-jet and W+jets normalization factors are found to be 1.4 +2.5 −1.4 and 0.98±0.30 respectively. Due to the small number of events in some of the ABCD regions, the uncertainty on the multi-jet normalization factor is large; however, the multi-jet contribution to the total background is very small and the effect on the total signal region background uncertainty is small.
Two multi-jet validation regions are defined with the same selection as for the signal region, but with t cut < 0.07 and intermediate m T2 . These multi-jet validation regions are enriched in events with jets misidentified as hadronic tau decays and good agreement is seen between the data and expectation across the BDT input kinematic variables. A further two validation regions are defined to check the modeling of the W+jets background. The intermediate BDT region −0.2 < t cut < 0.07 is used, with a high E miss T selection, where the W+jets background is seen to be modeled well. The validation region definitions are shown in Table 3. Table 4 and Figures 3(a), 3(b), 3(c), and 3(d) show the agreement between data and expectation in the validation regions. The purity of the multi-jet and W+jets validation regions is ∼90% and ∼50% respectively, while the signal contamination from the m(τ R ,χ 0 1 ) = (109,0) GeV scenario is <1% and <10% respectively.

Results
The observed number of events in the signal region is shown in Table 4 along with the background expectations, uncertainties, p 0 -value, S 95 exp , S 95 obs , ǫσ 95 obs , and the CL b value. The individual sources of uncertainty on the background estimation in the SR are shown in Table 5, where the dominant sources are the statistical uncertainty on the MC simulation samples, the uncertainty on the E miss T from energy deposits not associated with reconstructed objects and the statistical uncertainty on the normalization factor applied to the W+jets background. Generator modeling uncertainties for the W+jets background are estimated by varying the renormalization and factorization scales individually between 0.5 and 2 times the nominal values in Alpgen. Additionally, the impact of the jet p T threshold used for parton-jet matching in Alpgen W+jets simulation is assessed by changing the jet p T threshold from 15 GeV to 25 GeV. Figures 4(a), 4(b), 4(c), and 4(d) show the distributions of the BDT response prior to the t cut selection, and the E miss T , m eff and m T2 quantities in the SR, where good agreement between the expected background and the observed data is seen. Table 4: Numbers of events observed in data and expected from SM processes and the SUSY reference point m(τ R ,χ 0 1 ) = (109,0) GeV in the two-tau MVA validation and signal regions. The uncertainties shown include both statistical and systematic components. The "top" contribution includes the single top, tt, and ttV processes. The multi-jet background estimation is taken from data, as described in the text. In the VR, the multi-jet scale factor from fitting the background is not applied, while the W+jets scale factor is applied. In the SR, both the multi-jet and the W+jets scale factors are applied. Also shown are the model-independent limits calculated from the signal region observations: the one-sided p 0 -value; the expected and observed upper limit at 95% CL on the number of beyond-the-SM events (S 95 exp and S 95 obs ) for each signal region, calculated using pseudoexperiments and the CL s prescription; the observed 95% CL upper limit on the signal cross-section times efficiency ( ǫσ 95 obs ); and the CL b value for the background-only hypothesis.

SM process
Multi

Compressed spectra in direct production ofχ
In many SUSY scenarios, one or more of the mass differences between the charginos and neutralinos is small, resulting in final states with low-momentum leptons that require dedicated searches. The twolepton analysis in Ref. [19] excludedχ The analyses presented in this section focus on event selections based on low-momentum leptons, and also on the production in association with ISR jets to provide improved sensitivity to the compressed spectra scenarios not covered by previous searches. As discussed in Section 2, simplified models describingχ 0 2 production are considered for these compressed spectra searches, where theχ ± 1 /χ 0 2 decay only through sleptons or sneutrinos. The compressed spectra searches are less sensitive to scenarios where theχ ± 1 /χ 0 2 decay through SM W, Z or Higgs bosons, as the branching fraction to leptonic final states is significantly suppressed. The experimental sensitivity to these scenarios is expected to be recovered with a larger dataset.

Searches with two opposite-sign light leptons
Previous searches for directχ + 1χ − 1 production using two opposite-sign light-lepton final states are extended here to increase the sensitivity to compressed SUSY scenarios. The opposite-sign, two-lepton analysis presented here probesχ ± 1 -χ 0 1 mass splittings below 100 GeV using an ISR-jet selection.

Event selection
Events are reconstructed as described in Section 5, with the signal light-lepton p T threshold raised to p T = 10 GeV. In addition, in events where tagged light leptons form an SFOS pair with m SFOS < 12 GeV, both leptons in the pair are rejected. Events must have exactly two signal light leptons with opposite charge, and satisfy the symmetric or asymmetric dilepton trigger criteria, as described in Section 5.
To suppress the top-quark (tt and Wt) production contribution to the background, events containing central b-tagged jets or forward jets are rejected. To suppress events from Z boson decays, events with invariant mass of the reconstructed SFOS pair within 10 GeV of the Z boson mass (91.2 GeV) are rejected in the same-flavor channel.
Two SRs, collectively referred to as SR2ℓ-1, are defined. Both are designed to provide sensitivity tõ χ + 1χ − 1 production withl L -mediated decays and lowχ ± 1 -χ 0 1 mass splittings and rely on a high-p T ISR jet to boost the leptons, which would otherwise have too low momentum to be reconstructed. The superrazor variables that are discussed in Section 6.1 are used to discriminate between signal and backgrounds. Both the same-flavor (SF) and different-flavor (DF) channels are used. The first SR, SR2ℓ-1a, requires R 2 > 0.5(0.7) in the SF (DF) channel, whereas the second SR, SR2ℓ-1b, requires R 2 > 0.65 (0.75). Both SRs require M R ∆ > 20 GeV to reduce SM Z+jets background, and ∆φ β R > 2 (2.5) in the SF (DF) to further increase the signal sensitivity. Table 6 summarizes the complete definitions of the SRs. SR2ℓ-1a provides sensitivity for moderateχ

Background determination
The SM background is dominated by WW diboson and top-quark production. The MC predictions for these SM sources, in addition to contributions from ZV production, where V = W or Z, are normalized in dedicated control regions for each background. The reducible background is estimated using the matrix method as described in Section 6.2. Finally, contributions from remaining sources of SM background, which include Higgs boson production and Z+jets, are small and are estimated from simulation. These are collectively referred to as "Others".
The top CR is defined using the DF sample in order to suppress events from SM Z boson production.
Events are required to have exactly one central light-flavor jet with p T > 80 GeV, no forward jet, and M R ∆ > 20 GeV. At least one b-tagged jet is required to enrich the purity in top-quark production and ensure orthogonality to the SRs. Figures 5(a) and 5(b) show the M R ∆ and ∆φ β R distributions in this CR, respectively. The estimated signal contamination in this CR is less than 1% for the signal models considered.
The WW CR is also defined using the DF sample. Events are required to have exactly one central light jet, no forward jet or b-tagged jet, p ℓℓ T > 70 GeV, and M R ∆ > 20 GeV. In order to ensure orthogonality to the SRs, ∆φ β R < 2 is required. Figure 5(c) shows the R 2 distribution in this CR. The estimated signal contamination in this CR is less than 20% for the signal models considered.
The ZV CR is defined using the SF samples, and by requiring exactly one central light jet, no forward jet or b-tagged jet, p ℓℓ T > 70 GeV, ∆φ β R > 2 and M R ∆ > 20 GeV. In order to increase the purity in ZV production, events with invariant mass of the reconstructed SFOS pair within 10 GeV of the Z boson mass are used. This requirement also ensures orthogonality to the SRs. Figure 5(d) shows the p ℓℓ T distribution in this CR. The estimated signal contamination in this CR is less than 10% for the signal models considered.
A simultaneous likelihood fit to the top, WW and ZV CRs is performed to normalize the corresponding background estimates to obtain yields in the SR (as described in Section 6). Table 6 summarizes the definitions of the CRs, and Table 7 summarizes the numbers of observed and predicted events in these CRs, data/MC normalizations, and CR compositions obtained from the simultaneous fit. Systematic uncertainties affect the estimates of the backgrounds and signal event yields in the control and signal regions. A breakdown of the different sources of systematic uncertainty on the background estimate as described in Section 6.3 is shown in Table 8. Generator modeling uncertainties are estimated Table 7: Numbers of observed and predicted events in the opposite-sign, two-lepton control regions, data/MC normalization factors, and composition of the CRs obtained from the background-only fit. The "Others" background category includes Z+jets and SM Higgs boson production. The Z+jets production is the dominant contribution to this category in the CR2ℓ-ZV.

Results
The observed number of events in each signal region is shown in Table 9 along with the background expectations and uncertainties, p 0 -values, S 95 exp , S 95 obs , ǫσ 95 obs , and the CL b values. Figures 6(a), 6(b), 6(c) and 6(d) show the distributions of the quantities R 2 and M R ∆ in the SR2ℓ-1a and SR2ℓ-1b regions respectively, prior to the requirements on these variables. For illustration, the distributions are also shown for twoχ + 1χ − 1 simplified models withl L -mediated decays and different mass splittings. Table 9: Observed and expected number of events in the opposite-sign two-lepton signal regions. The "Others" background category includes Z+jets and SM Higgs boson production. The numbers of signal events are shown for theχ + 1χ − 1 simplified models withl L -mediated decays and differentχ ± 1 andχ 0 1 masses in GeV. The uncertainties shown include both statistical and systematic components. Also shown are the model-independent limits calculated from the opposite-sign two-lepton signal region observations: the one-sided p 0 values; the expected and observed upper limits at 95% CL on the number of beyond-the-SM events (S 95 exp and S 95 obs ) for each signal region, calculated using pseudoexperiments and the CL s prescription; the observed 95% CL upper limit on the signal cross-section times efficiency ( ǫσ 95 obs ); and the CL b value for the background-only hypothesis. SR SR2ℓ-1a SR2ℓ-1b

Searches with two same-sign light leptons
In compressed mass scenarios, one or more of the three leptons fromχ ± 1χ 0 2 production may have momentum too low to be reconstructed. Therefore, the search forχ ± 1χ 0 2 production using two same-sign leptons can complement the three-lepton search documented in Ref. [20] and extend the reach for small mass splittings. The search for same-sign lepton pairs is preferable to opposite-sign pairs, due to the comparatively small SM background. A multivariate analysis technique is used here to discriminate between signal and backgrounds.

Event selection
Events are selected using the basic reconstruction, object and event selection criteria described in Section 5. In addition, if tagged light leptons form an SFOS pair with m SFOS < 12 GeV, both leptons in the pair are rejected. Signal electrons with p T < 60 GeV have a tightened track (calorimeter) isolation of 7% (13%) of the electron p T applied, whereas for electrons with p T > 60 GeV, a track isolation requirement of 4.2 GeV (7.8 GeV) is used. For signal muons, the track (calorimeter) isolation requirement is tightened to 6% (14%) of the muon p T for p T < 60 GeV, and 4.2 GeV (8.4 GeV) otherwise. The stricter lepton isolation requirements are optimized to suppress the reducible SM backgrounds with semileptonically decaying b/c-hadrons, which are an important background in this search.
Events must have exactly two light leptons with the same charge, e ± e ± , µ ± µ ± or e ± µ ± and satisfy the symmetric or asymmetric dilepton trigger criteria, as described in Section 5. Eight BDTs are independently trained to define eight signal regions optimized for four mass splitting scenarios, m(χ and ∆φ(ℓ, ℓ). Three further variables are also considered for the ISR signal regions: ∆φ(E miss T , jet1) and the ratios E miss,rel T /p jet1 T and p lep1 T /p jet1 T . These variables exploit the kinematic properties of a compressed mass SUSY system, with and without a high-p T ISR jet. The MC simulation samples are compared to data for these variables and their correlations to ensure that they are modeled well.
For the training and testing of the BDT, the signal and background samples are split into two halves, including those backgrounds estimated from data as described in Section 8.2.2. The eight signal region definitions are shown in Table 10. Since the selection on the BDT output, t cut , is independent for each SR, the overlap between SRs with looser and tighter selections is small.

Background determination
Several SM processes produce events with two same-sign signal leptons. The SM background processes are classified as irreducible background if they lead to events with two real, prompt, same-sign leptons, reducible background if the event has at least one fake or non-prompt lepton, or "charge flip" if the event has one lepton with mismeasured charge.
Irreducible processes include diboson (W ± W ± , WZ, ZZ), triboson (VVV), ttV, tZ and Higgs boson production and are determined using the corresponding MC samples. The reducible Wγ process is estimated with MC simulation samples; other reducible processes are estimated with the matrix method, similar to that described in Section 6.2.
In this implementation of the matrix method, the fake and non-prompt lepton misidentification probabilities are measured in control regions that are kinematically close and similar in composition to the signal regions. The regions where the misidentification probabilities are measured are required to have large H T (H T > 50 GeV) and large transverse mass using the leading lepton (m T > 50 GeV). The contamination from signal events in these measurement regions is <1%. The charge-flip, irreducible, and Wγ backgrounds are subtracted from the control regions before calculating lepton misidentification probabilities.
Charge-flip processes include sources of opposite-sign prompt leptons for which the charge of one lepton is mismeasured (Z, tt, W + W − ). In the relevant momentum range the muon charge-flip background is found to be negligible. Control samples of e + e − and e ± e ± with invariant mass near the Z boson mass (75< m ℓℓ < 100 GeV) are used to extract the electron charge-flip rate. A small background due to misidentified jets is subtracted by interpolating the mass sidebands and subtracting them from the observed data events. A likelihood fit is used that takes the numbers of e + e − and e ± e ± pairs observed in the charge-flip control regions as input. The charge-flip probability is a free parameter of the fit and is extracted as a function of the electron p T and η. The charge-flip background event yield is found by applying the charge-flip probability to control regions in data with the same kinematic requirements as the signal and validation regions, but with opposite-sign light lepton pairs. The contamination from fake and non-prompt leptons, and from signal events, is negligible in the e + e − and e ± e ± control regions.
Generator modeling uncertainties for the diboson processes are estimated by comparing the results from the Powheg Box and MC@NLO event generators, while parton showering uncertainties are estimated by comparing MC@NLO +Herwig with MC@NLO +Pythia. The impact of the choice of renormalization and factorization scales is evaluated by varying these individually between 0.5 and 2 times the nominal values in aMC@NLO for diboson events.
To test the background prediction methods, two validation regions with looser selection on the BDT output than the SRs are defined; the definitions are shown in Table 10. The light-lepton flavor content (ee, µµ, or eµ) is checked separately in each validation region. Table 11

Results
The observed number of events in each signal region is shown in Table 12 along with the background expectation and uncertainties, p 0 -values, S 95 exp , S 95 obs , ǫσ 95 obs , and the CL b values. No significant excess with respect to the SM expectation is observed. The sizes and sources of uncertainty on the background estimation in the signal regions are shown in Table 13, where the dominant sources of uncertainty are the statistical uncertainty on the reducible background estimation, the statistical uncertainty on the MC simulation samples, and the uncertainty related to the choice of generator for the WZ MC simulation sample.

Searches with three light leptons
Previous searches forχ ± 1χ 0 2 production using the three-lepton final state are extended here to increase the sensitivity to compressed SUSY scenarios. The three-lepton analysis presented here probesχ 0 2 -χ 0 1 mass splittings below 25 GeV using low-p T leptons and ISR jets.

Event selection
Events are selected as described in Section 5. In addition, signal muons with p T < 15 GeV have tightened track and calorimeter isolation requirements of 7% of the muon p T . The stricter muon isolation requirements suppress SM backgrounds with semileptonically decaying b/c-hadrons, which are larger for muons rather than electrons due to the lower muon-p T threshold. Events must satisfy a single-lepton, dilepton, or trilepton trigger.
Four signal regions are defined with exactly three light leptons, all with p T < 30 GeV, and at least one SFOS pair present among the leptons. All signal regions veto events with b-tagged jets to reduce the tt SM background and events with 8.4 < m SFOS < 10.4 GeV to suppress backgrounds with leptonic Υ decays. The three-lepton signal region selections are summarized in Table 14.
The first two signal regions, SR3ℓ-0a and SR3ℓ-0b, closely follow the selection in Ref. [20], using E miss T , m T and m SFOS selections. SR3ℓ-0a and SR3ℓ-0b are defined with E miss T > 50 GeV and 30 < m ℓℓℓ < 60 GeV to reject diboson processes. Events with a jet with p T > 50 GeV are vetoed to be disjoint from the ISR signal region. The first signal region, SR3ℓ-0a, targets the smallestχ GeV. The third and fourth signal regions, SR3ℓ-1a and SR3ℓ-1b, both require the presence of a p T > 50 GeV jet to target signal production with ISR. The leptons from a compressed SUSY decay chain would have too low p T to be reconstructed; however, due to the recoil against the high-p T ISR jet, all three leptons can be boosted enough to meet the selection requirements. The third signal region, SR3ℓ-1a, targets the smallestχ 0 2 -χ 0 1 mass splittings and selects events with 5 < m min SFOS < 15 GeV. Here the leading jet is required to be back-to-back in the transverse plane with the E miss T , ∆φ(E miss T , jet 1) > 2.7 rad, and the ratio of leading lepton p T to the jet p T is required to be small, p lep 1 T /p jet 1 T < 0.2, to suppress the diboson and tt backgrounds. The fourth signal region, SR3ℓ-1b, targets the slightly largerχ 0 2 -χ 0 1 mass splittings by selecting events with 15 < m min SFOS < 25 GeV. To suppress the WZ and tt backgrounds in SR3ℓ-1b, the angle between the E miss T and the three-lepton system is required to be large, ∆φ(E miss T , 3ℓ) > 0.7π rad.

Background determination
Several SM processes produce events with three signal leptons. The SM background processes are classified as irreducible background if they lead to events with three or more real leptons, or as reducible background if the event has at least one fake or non-prompt lepton. The predictions for irreducible and reducible backgrounds are tested in validation regions. For this search, irreducible processes include diboson (WZ and ZZ), VVV, ttV, tZ and Higgs boson production and are determined from MC simulation samples.
Reducible processes include single-and pair-production of top quarks, WW production and a single W or Z boson produced in association with jets or photons. The dominant reducible background component is tt, followed by Z+jets. The reducible background is estimated using the matrix method, similar to that described in Section 6.2. In this implementation of the matrix method, the highest-p T signal electron or muon is taken to be real and only the second and third leptons are used in the matrix method. Simulation studies show that neglecting the case that the leading lepton is non-prompt or fake is valid in more than 95% of the events.
The uncertainty on the reducible background includes the MC statistical uncertainty on the weights for the process-dependent misidentification probabilities, the uncertainty on the correction factors for the misidentification probability, the statistical uncertainty on the data events to which the matrix equation is applied and the statistical uncertainty from the misidentification probability measured in simulation.
The systematic uncertainty related to the theoretical modeling of the WZ and ZZ backgrounds is assessed by comparing MC estimates with data in dedicated regions. The WZ region requires three light leptons with p T > 30 GeV, an SFOS pair among the three leptons, 30< E miss T < 50 GeV and one jet with p T > 50 GeV. Events with an SFOS pair or three-lepton invariant mass within 10 GeV of the Z boson mass are vetoed. The ZZ region is defined with four light leptons with p T > 10 GeV, two SFOS pairs with invariant mass within 10 GeV of the Z boson mass and E miss T < 50 GeV. This approach for estimating the systematic uncertainties is used here instead of the MC-based approach discussed in Section 6.3. The WZ and ZZ MC simulation samples are both found to agree with observations in the dedicated regions within 15%, which is applied as a systematic uncertainty in the three-lepton validation and signal regions.
The background predictions are tested in validation regions that are defined to be adjacent to, yet disjoint from, the signal regions. Low-E miss T validation regions ("a" regions) and high-E miss T + b-jet validation regions ("b" regions) are defined to target different background processes. The definition of the regions and the targeted processes are shown in Table 15. In the three-lepton validation regions, the observed data counts and SM expectations are in good agreement within statistical and systematic uncertainties, as shown in Table 16 and Figures 8(a), 8(b), 8(c), and 8(d).

Results
The observed number of events in each signal region is shown in Table 17 along with the background expectations and uncertainties, p 0 -values, S 95 exp , S 95 obs , ǫσ 95 obs , and the CL b values. The sizes and sources of uncertainty on the background estimation in the three-lepton signal regions are shown in Table 18, where the dominant sources of uncertainty are the statistical uncertainty on the data for the reducible background estimate, and the uncertainty on the electron and muon misidentification probabilities. Figures 9(a), 9(b), 9(c) and 9(d) show the distributions of the quantities E miss T , m ℓℓℓ , ∆φ(E miss T , jet 1) and p jet 1 T in SR3ℓ-0a, SR3ℓ-0b, SR3ℓ-1a and SR3ℓ-1b regions respectively, prior to the requirements on these variables. For illustration, the distributions are also shown for aχ ± 1χ 0 2 scenario withl L -mediated decays, where the slepton mass is set halfway between theχ ± 1 and theχ 0 1 masses. Table 17: Expected and observed yields in the three-lepton signal regions. The uncertainties shown include both statistical and systematic components. The "Others" background category includes ttV, VVV and SM Higgs boson production. Also shown are the model-independent limits calculated from the three-lepton signal region observations: the one-sided p 0 -values; the expected and observed upper limits at 95% CL on the number of beyond-the-SM events (S 95 exp and S 95 obs ) for each signal region, calculated using pseudoexperiments and the CL s prescription; the observed 95% CL upper limit on the signal cross-section times efficiency ( ǫσ 95 obs ); and the CL b value for the background-only hypothesis.

Same-sign chargino-pair production via vector-boson fusion
This section presents a search for the same-sign chargino-pair production via VBF with subsequentl Lmediated chargino decays into final states with two same-sign light leptons, at least two jets and E miss T . Although the cross-section for VBF production is significantly lower than that for direct production, the two additional jets in the event provide a means to separate the signal from the background for compressed spectra scenarios, and complement the direct production searches that use low-momentum leptons and ISR jets.

Event selection
Events are selected using the basic reconstruction, object and event selection criteria described in Section 5. In addition, signal muons with p T < 15 GeV have tightened isolation requirements as in the threelepton analysis described in Section 8.3. A tighter isolation is needed for muons rather than electrons due to the lower p T threshold for muons. The stringent lepton isolation suppresses the dominant reducible background processes. Events are required to satisfy an E miss T trigger.
One signal region, SR2ℓ-2, is defined with exactly two same-sign light leptons, at least two jets (central light or forward) and large missing transverse momentum E miss T > 120 GeV. In order to select events that originate from VBF production, the highest-p T jet (jet 1) and the second highest-p T jet (jet 2) are required to have large invariant mass, m j j > 350 GeV, be well separated in pseudorapidity, |∆η j j | > 1.6, and be in opposite sides of the detector, η jet 1 · η jet 2 < 0. The last requirement greatly reduces the SM background originating from non-VBF diboson and Higgs boson production. The residual SM background originating from diboson and top-quark production is minimized by requiring the events to have no b-tagged jets, moderate invariant mass of the two leptons (m ℓℓ < 100 GeV), small stransverse mass (m T2 < 40 GeV) and a high-p T jet (p jet 1 T > 95 GeV). In addition, requirements are made on the ratios of the jet p T , E miss T , p j j T and p ℓℓ T . The SR definition is summarized in Table 19.

Background determination
Several SM processes lead to events with two same-sign signal leptons. The irreducible background is dominated by diboson production, which is estimated using MC simulation samples. The dominant reducible background component is from W+jets production, followed by tt production, and these are estimated using a data-driven technique called the "fake factor method", similar to that described in Ref. [116]. The production of Wγ is also an important background component, and is modeled using MC simulation samples. The charge-flip background is estimated by applying data-driven corrections to the MC simulation samples, following the procedure outlined in Section 8.2.2.
The fake factor method estimates the contributions from processes that produce one or two fake or nonprompt leptons using data events that contain one signal lepton and one lepton failing to satisfy the signal lepton requirements. These events are scaled by a "fake factor" to predict the reducible background in the signal region. The fake factor is defined as the ratio of events with two signal leptons to events with one signal lepton and one lepton failing the signal lepton requirements. It is measured in data using a control sample of jets faking leptons in Z → ℓℓ events. The SM background process dependence of the fake factor is studied using simulation, and no strong dependence is observed. Residual differences are covered by assigning a 30% uncertainty, independent of the lepton p T , to the fake factor. The uncertainty on the reducible background estimate ranges from 37% to 42%, depending on the channel (ee, µµ or eµ), and is dominated by the prompt lepton contamination in the control sample and the uncertainty on the extrapolation of fake factors into the signal region.
The contributions from diboson processes are estimated using MC simulation samples. Sherpa is used to produce all diboson samples, taking into account both the strong and electroweak production of associated jets. The W ± W ± +2jets and WZ+2jets processes are normalized to NLO cross-sections using corrections evaluated in dedicated VBF fiducial regions at the parton level. The corrections are calculated separately for strong and electroweak jet production. For the W ± W ± +2jets production, the fiducial cross-section is calculated using Powheg Box +Pythia [62,63,117] and the fiducial region is defined to be identical to the signal region at the parton level, except for the lepton isolation requirement. For the WZ+2jets production, the fiducial cross-sections are calculated using VBFNLO-2.7.0 [118]. Since it is not possible to define a fiducial region that is identical to the signal region using VBFNLO-2.7.0, a looser set of requirements is imposed. The generator modeling uncertainty is estimated by comparing Powheg Box +Pythia with VBFNLO-2.7.0 for W ± W ± +2jets production, and parton showering uncertainties are estimated by comparing Powheg Box +Herwig with Powheg Box +Pythia. The impact of the choice of renormalization and factorization scales is evaluated by varying each between 0.5 and 2 times the nominal values. The uncertainties due to the PDFs are evaluated using 90% CL CT10 PDF eigenvectors. Finally, the interference between the strong and electroweak jet production is studied at LO accuracy using Sherpa and is found to have a negligible effect on the combined fiducial cross-section in the signal region.
The background predictions are tested in VRs that are defined to be as kinematically close to the SR as possible. The first VR, VR-Fakes, is defined with two signal light leptons, large E miss T and at least two jets to test backgrounds with fake and non-prompt leptons modeled by the fake factor method. The second VR, VR-VV, adopts the same requirements as the VR-Fakes, in addition to higher lepton-p T thresholds and a b-jet veto that allow it to test the MC modeling of the diboson background. By definition, the VRs are not disjoint from the SR, but have negligible overlaps. The overlap between the VR-Fakes (VR-VV) and the SR is 2.4% (0.2%) and the largest signal contamination is 1.9% (0.9%) of the total expected background in the VR-Fakes (VR-VV). The definitions of the validation regions are shown in Table 20, along with the targeted processes. The yields in the VRs are shown in Table 21, where the background expectation is in good agreement with the observed data, within the total uncertainties. Figures 10(a)

Results
The observed number of events in the signal region is shown in Table 21 along with the background expectation and uncertainties, p 0 -value, S 95 exp , S 95 obs , ǫσ 95 obs , and the CL b value. No significant excess with respect to the SM expectation is observed. A breakdown of the different sources of systematic uncertainty in the signal region, including those described in Section 6.3, is shown in Table 22. Figures 11(a)  andχ 0 1 masses in GeV. The uncertainties shown include both statistical and systematic components. The modelindependent limits are also shown: the one-sided p 0 value; the expected and observed upper limit at 95% CL on the number of beyond-the-SM events (S 95 exp and S 95 obs ) for the signal region, calculated using pseudoexperiments and the CL s prescription; the observed 95% CL upper limit on the signal cross-section times efficiency ( ǫσ 95 obs ); and the CL b value for the background-only hypothesis.

Interpretation of results
Previous ATLAS searches for EW SUSY production [19][20][21][22][23] are combined with the new analyses presented in Sections 7-9. The combined results are interpreted in the SUSY models discussed in Section 2. The analyses combined for each SUSY model are shown in Table 23. Limits in the simplified models targeted by the analysis presented in the previous sections are presented in Sections 10.1-10.4. A summary is provided in Section 10.5, including the limits previously obtained from the ATLAS searches forχ production with WW-mediated decays [19],χ ± 1χ 0 2 production with WZ-mediated decays [20] andχ ± 1χ 0 2 production with Wh-mediated decays [23]. Finally, limits on phenomenological models are presented in Sections 10.6-10.8. For these models, the new searches presented in this article are not included, since they target very specific areas of parameter space and their sensitivity is small.
Exclusion limits are calculated by statistically combining results from a number of disjoint signal regions.
In general, the analyses in Table 23 are mutually exclusive by design (the exceptions are indicated in the table), using the lepton multiplicity and charge, and are statistically combined. Where overlapping signal regions exist within an analysis, the signal region with the best-expected exclusion is used. During the combinations, all experimental uncertainties are treated as correlated between regions and processes, with the exception of the experimental uncertainties on data-driven backgrounds, which are correlated between regions only. Theoretical uncertainties on the irreducible background and signal are treated as correlated between regions, while statistical uncertainties are treated as uncorrelated between regions and processes. For the exclusion limits, the observed and expected 95% CL limits are calculated using asymptotic formulas for each SUSY model point, taking into account the theoretical and experimental uncertainties on the SM background and the experimental uncertainties on the signal. Where the threelepton [20] analysis is used in the combination, 95% CL limits are calculated using pseudoexperiments as the asymptotic approximation becomes inappropriate where the expected and observed yields are close to zero. The impact of the theoretical uncertainties on the signal cross-section is shown for the observed mass limit; where quoted in the text, mass limits refer to the −1σ variation on the observed limit. Table 23: Searches used to probe each of the models described in Section 2.

Direct stau production
The combination of the two-tau MVA results in Section 7 with the simple cut-based analysis from Ref. [22] is used to set limits on the direct production of stau pairs. For each signal point, the signal region with the best expected limit is used. The upper limits on the cross-section for direct stau production are shown in Figure 12 for combinedτ LτL andτ RτR production, where the observed limit is nearly always above the theoretical prediction. One scenario of combinedτ LτL andτ RτR production is excluded, where theτ R mass is 109 GeV and theχ 0 1 is massless. For this scenario, cross-sections above 0.115 pb are excluded, where the theoretical cross-section at NLO is 0.128 pb. No scenarios can be excluded where onlyτ RτR production orτ LτL production is considered. Cross-sections above 0.06 (0.21) pb are excluded forτ RτR (τ LτL ) production with aτ R (τ L ) mass of 109 GeV and a masslessχ 0 1 , where the theoretical crosssection at NLO is 0.04 (0.09) pb. For this scenario [m(τ R ) = 109 GeV, m(χ 0 1 ) = 0 GeV], the expected yields fromτ RτR production are larger than fromτ LτL in the signal region, making the experimental limits stronger forτ RτR production. However, for other mass points the experimental limit is generally weaker forτ RτR production due to the lower production cross-section. These limits on direct production of stau pairs improve upon the previous limits in Ref. [22], particularly for stau masses below ∼150 GeV. [pb]

Direct chargino production
The opposite-sign, two-lepton analysis in Ref. [19] is used to reinterpret the limits onχ where the slepton mass is 5%, 25%, 50%, 75% and 95% of theχ ± 1 mass are studied for a masslessχ 0 1 , and the limits are shown in Figure 13(a). For the majority of theχ ± 1 masses considered, the slepton mass does not have a significant effect on the sensitivity andχ ± 1 masses are excluded up to ∼500 GeV. The sensitivity is reduced for a very small mass splitting between the chargino and the slepton (x = 0.95), as in this case leptons from theχ ± 1 →νℓ decays have low momentum, making these events difficult to reconstruct in the two lepton final state.
Limits are also set in theχ  Figure 13(b) shows the opposite-sign, two-lepton analysis presented in Section 8.1, which provides new sensitivity to compressed scenarios forχ ± 1 masses below ∼220 GeV. The 2ℓ analysis in Ref. [19] continues to dominate the sensitivity to scenarios with large mass splittings, excludingχ ± 1 masses up to ∼465 GeV.
[GeV]   [19], while the limits in (b) use the opposite-sign, two-lepton analysis from this article. The limit from Ref. [19] is also shown in (b).
The same-sign, two-lepton VBF analysis described in Section 9 is used to set limits on VBFχ masses, since these scenarios were used for optimizing the signal selection.

Direct neutralino-chargino production
The three-lepton analysis in Ref. [20] is used to reinterpret the limits onχ ± 1χ 0 2 production decaying through sleptons. Scenarios where the slepton mass is 5%, 25%, 50%, 75% and 95% of theχ Limits are also set in theχ ± 1χ 0 2 scenarios withl L -mediated decays, with slepton masses set halfway and at 95% between theχ  17(b) show that the combination of the published and new analyses gives an improved sensitivity to compressed scenarios up toχ ± 1 masses of ∼250 GeV. In scenarios with large mass splittings,χ ± 1 masses are excluded up to ∼700 GeV for slepton masses set to theχ 0 1 mass plus 50% or 95% of the difference between theχ ± 1 and theχ 0 1 masses. In the compressed areas of theχ ± 1χ 0 2 scenario withl L -mediated decays, and slepton masses set halfway (95%) between theχ ± 1 and theχ 0 1 masses, the three-lepton (same-sign, two-lepton) analysis has the strongest sensitivity.
Finally, limits are set in theχ ± 1χ 0 2 scenario withτ-mediated decays, using combined results from the twotau analysis in Ref. [22] and the three-lepton analysis in Ref. [20]. Figure 18 shows that the sensitivity to largeχ is massless and the intermediate slepton mass is set to 5%, 25%, 50%, 75%, and 95% of theχ ± 1 mass. The limits are set using the 3ℓ analysis from Ref. [20].
[GeV]  [20] and the same-sign, two-lepton anaysis from this article, while the limits in (b) use the combination of the three-lepton and same-sign, two-lepton anayses from this article.  masses. The limits are set using a combination of the 3ℓ analysis from Ref. [20] and the 2τ analysis from Ref. [22].

Summary of simplified electroweakino production
The ATLAS results for electroweakino searches at 8 TeV in the framework of simplified models are summarized in Figures 19(a) and 19(b) in the m(χ  Figure 19(a). All of the limits are from the two-lepton, three-lepton, and Wh analyses from Refs. [19,20,23]. The new analyses targeting compressed spectra presented in this article only have a small sensitivity to these scenarios and did not significantly improve upon published limits. The limits forχ

pMSSM
The two-lepton, three-lepton, and Wh analyses from Refs. [19,20,23] are combined to improve the sensitivity in the considered pMSSM scenario where the EW SUSY production and the decays through W, Z, or h bosons are dominant. The 95% CL exclusion in the pMSSM µ-M 2 plane for the scenario of heavy sleptons, tan β = 10, and M 1 = 50 GeV is shown in Figure 20. Including the Wh analysis in the new combination results in a stronger limit at high values of M 2 , in particular in the intermediate µ region.
[GeV] µ All limits at 95% CL Figure 20: The 95% CL exclusion limit in the pMSSM scenario, using a combination of the 2ℓ and 3ℓ analyses from Ref. [19] and the Wh analysis from Ref. [23]. The areas excluded by the −1σ expected limit are shown in green. The blue contour corresponds to the limits from the combination of the 2ℓ and 3ℓ analyses from Ref. [19]. The grey dotted contours show the chargino mass isolines.

NUHM2
The two-, three-and four-lepton analyses from Refs. [19][20][21] are combined to set limits in a new interpretation for the NUHM2 model. The 95% CL exclusion in the NUHM2 m 1/2 -µ plane is shown in Figure 21, where the three-lepton analysis offers the best sensitivity and drives the combined limit. The results in the three-lepton signal regions lead to a weaker observed exclusion than expected for the compressed scenarios in the high-m 1/2 , low-µ region. In general, m 1/2 values up to 300 GeV are excluded in the NUHM2 model. l Observed limit 2 l Observed limit 3 l Observed limit 4 All limits at 95% CL Figure 21: The 95% CL exclusion limit in the NUHM2 scenario, using a combination of the 2ℓ, 3ℓ and 4ℓ analyses from from Refs. [19][20][21]. The areas excluded by the −1σ expected limit are shown in green. The black, pink and blue contours correspond to the limits from the 2ℓ, 3ℓ and 4ℓ analyses respectively.

GMSB
The four-lepton analysis from Ref. [21] is reinterpreted in the GMSB model described in Section 2. The 95% CL exclusion in the GMSB Λ-tan β plane is shown in Figure 22  Observed limit All limits at 95% CL Figure 22: The 95% CL exclusion limit in the GMSB scenario, using the 4ℓ analysis from Ref. [21]. The green contour corresponds to the limit from the 2SS/3ℓ+jets analysis from Ref. [119].

Conclusion
This article summarizes and extends the search for the production of electroweak SUSY particles using 20 fb −1 of √ s = 8 TeV pp collision data collected with the ATLAS detector at the LHC. New analyses targeting scenarios with compressed mass spectra, VBF production of charginos and neutralinos, and the direct production of stau pairs provide sensitivity to EW SUSY scenarios not optimally covered in previous publications. The new and previous results are combined to set exclusion limits in a wide range of simplified and phenomenological SUSY models. Forχ For all threel L -mediated decay scenarios, the value of the slepton mass is not seen to have a significant effect on the sensitivity. Exclusions are also set in pMSSM, NUHM2, and GMSB models, improving upon previous limits.