Search for direct top-squark pair production in final states with two leptons in pp collisions at sqrt(s)=8TeV with the ATLAS detector

A search is presented for direct top-squark pair production in final states with two leptons (electrons or muons) of opposite charge using 20.3fb-1 of pp collision data at sqrt(s)=8TeV, collected by the ATLAS experiment at the Large Hadron Collider in 2012. No excess over the Standard Model expectation is found. The results are interpreted under the separate assumptions (i) that the top squark decays to a b-quark in addition to an on-shell chargino whose decay occurs via a real or virtual W boson, or (ii) that the top squark decays to a t-quark and the lightest neutralino. A top squark with a mass between 150 GeV and 445 GeV decaying to a b-quark and an on-shell chargino is excluded at 95% confidence level for a top squark mass equal to the chargino mass plus 10 GeV, in the case of a 1 GeV lightest neutralino. Top squarks with masses between 215 (90) GeV and 530 (170) GeV decaying to an on-shell (off-shell) t-quark and a neutralino are excluded at 95% confidence level for a 1 GeV neutralino.


Introduction
Supersymmetry (SUSY) [1][2][3][4][5][6][7][8][9] is an extension to the Standard Model (SM) which introduces supersymmetric partners of the known fermions and bosons. For each known boson or fermion, SUSY introduces a particle with identical quantum numbers except for a difference of half a unit of spin (S). The introduction of gauge-invariant and renormalisable interactions into SUSY models can violate the conservation of baryon number (B) and lepton number (L), -1 -resulting in a proton lifetime shorter than current experimental limits [10]. This is usually solved by assuming that the multiplicative quantum number R-parity (R), defined as R = (−1) 3(B−L)+2S , is conserved. In the framework of a generic R-parity-conserving minimal supersymmetric extension of the SM (MSSM) [11][12][13][14][15], SUSY particles are produced in pairs where the lightest supersymmetric particle (LSP) is stable, and is a candidate for dark matter.
In a large variety of models, the LSP is the lightest neutralino (χ 0 1 ). The scalar partners of right-handed and left-handed quarks (squarks),q R andq L , mix to form two mass eigenstates, q 1 andq 2 , withq 1 defined to be the lighter one. In the case of the supersymmetric partner of the top quark (top squark,t), large mixing effects can lead to one top-squark mass eigenstate, t 1 , that is significantly lighter than the other squarks. Consideration of naturalness and its impact on the SUSY particle spectrum, suggests that top squarks cannot be too heavy, to keep the Higgs boson mass close to the electroweak scale [16,17]. Thust 1 could be pair-produced with relatively large cross-sections at the Large Hadron Collider (LHC).
The top squark can decay into a variety of final states, depending, amongst other factors, on the hierarchy of the mass eigenstates formed from the linear superposition of the SUSY partners of the Higgs boson and electroweak gauge bosons. In this paper the relevant mass eigenstates are the lightest chargino (χ ± 1 ) and theχ 0 1 . Two possible sets of SUSY mass spectra are considered, assuming that the mixing of the neutralino gauge eigenstates is such that theχ 0 1 is mostly the supersymmetric partner of the SM boson B (before electroweak symmetry breaking) and taking into account previous experimental constraints from the LEP experiments [18] that m(χ ± 1 ) > 103. 5 GeV. In both sets of spectra (figure 1) thet 1 is the only coloured particle contributing to the production processes. In the first scenario thet 1 , assumed to bet L , decays viat 1 → b +χ ± 1 , where m(t 1 ) − m(χ ± 1 ) > m(b), and theχ ± 1 (assumed to be mostly the supersymmetric partner of the SM W boson before electroweak symmetry breaking) subsequently decays into the lightest neutralino (assumed to be the LSP) and a real (figure 1 (a)) or virtual (figure 1 (b)) W boson. In the second scenario (figure 1 (c)), thet 1 , assumed to be 70%t R , decays viã t 1 → t +χ 0 1 . Both on-shell, kinematically allowed for m(t 1 ) > m(t) + m(χ 0 1 ), and off-shell (resulting in a three-body decay to bWχ 0 1 ) top quarks are considered. In all scenarios the top squarks are pair-produced and, since only the leptonic decay mode of the W ( * ) is considered, the events are characterised by the presence of two isolated leptons (e, µ) 1 with opposite charge, and two b-quarks. Significant missing transverse momentum p miss T , whose magnitude is referred to as E miss T , is also expected from the neutrinos and neutralinos in the final states.
In this paper, three different analysis strategies are used to search fort 1 pair production, with a variety of signal regions defined for each. Two of the analyses target thet 1 → b +χ ± 1 decay mode and the three-bodyt 1 → bWχ 0 1 decay via an off-shell top-quark, whilst one targets thet 1 → t +χ 0 1 to an on-shell top-quark decay mode. The kinematics of thet 1 → b +χ ± 1 decay mode depend upon the mass hierarchy of thet 1 , 1 Electrons and muons from τ decays are included.
-2 -χ ± 1 andχ 0 1 particles (figure 1 (a) and 1 (b)). In order to be sensitive to all the possible mass splittings, two complementary cut-based analysis strategies are designed: one to target largẽ χ ± 1 −χ 0 1 mass splittings (larger than the W bosons mass), and one to target smallχ ± 1 −χ 0 1 mass splittings (smaller than the W bosons mass); the first one provides the sensitivity to thet 1 three-body decay. These signatures have both very small cross-section and low branching ratios (BRs) (of top-quark pairs to dileptonic final states). A multivariate approach is used to target the on-shell topt 1 → t +χ 0 1 decay mode (figure 1 (c)), to enhance sensitivity beyond what can be achieved with cut-and-count techniques.  Figure 1. Schematic diagrams of mass hierarchy for thet 1 → b +χ ± 1 decay mode ((a) larger than the W mass (χ ± 1 ,χ 0 1 ) mass splitting and (b) smaller than the W mass (χ ± 1 ,χ 0 1 ) mass splitting), and (c) thet 1 → tχ 0 1 decay mode.
Previous ATLAS analyses using data at √ s = 7 TeV and 8 TeV have placed exclusions limits at 95% confidence level (CL) on both thet 1 → b +χ ± 1 [19][20][21] andt 1 → t +χ 0 1 [22-24] decay modes. This search is an update of the 7 TeV analysis targeting the two-lepton final state [24] with a larger dataset, including additional selections sensitive to various signal models and exploiting a multivariate analysis technique. Limits on top squarks direct production have also been placed by the CMS [25-28], CDF [29] and D0 [30] collaborations.

The ATLAS detector
ATLAS is a multi-purpose particle physics experiment [31] at the LHC. The detector layout 2 consists of inner tracking devices surrounded by a superconducting solenoid, electromagnetic 2 ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the centre of the detector and the z-axis coinciding with the axis of the beam pipe. The x-axis points from the IP to the centre 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 beam pipe. The pseudorapidity is defined in terms of the polar angle θ as η = − ln tan(θ/2). and hadronic calorimeters and a muon spectrometer. The inner tracking detector (ID) covers |η| < 2.5 and consists of a silicon pixel detector, a semicondictor microstrip detector, and a transition radiation tracker. The ID is surrounded by a thin superconducting solenoid providing a 2T axial magnetic field and it provides precision tracking of charged particles and vertex reconstruction. The calorimeter system covers the pseudorapidity range |η| < 4.9. In the region |η| < 3.2, high-granularity liquid-argon electromagnetic sampling calorimeters are used. A steel/scintillator-tile calorimeter provides energy measurements for hadrons within |η| < 1.7. The end-cap and forward regions, which cover the range 1.5 < |η| < 4.9, are instrumented with liquid-argon calorimeters for both electromagnetic and hadronic particles. The muon spectrometer 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).

Monte Carlo simulations and data samples
Monte Carlo (MC) simulated event samples are used to model the signal and to describe all the backgrounds which produce events with two prompt leptons from W , Z or H decays. All MC samples utilised in the analysis are produced using the ATLAS Underlying Event Tune 2B [32] and are processed through the ATLAS detector simulation [33] based on GEANT4 [34] or passed through a fast simulation using a parameterisation of the performance of the ATLAS electromagnetic and hadronic calorimeters [35]. Additional pp interactions in the same (intime) and nearby (out-of-time) bunch crossings (pile-up) are included in the simulation.
Top-quark pair and W t production are simulated with MC@NLO-4.06 [44,45], interfaced with HERWIG-6.520 [46] for the fragmentation and the hadronisation processes, and using JIMMY-4.31 [47] for the underlying event description. In addition, ACERMC-3.8 [48] samples and POWHEG-1.0 [49] samples, interfaced to both PYTHIA-6.426 and HERWIG-6.520, are used to estimate the event generator, fragmentation and hadronisation systematic uncertainties. Samples of ttZ and ttW production (referred to as ttV ) are generated with MADGRAPH-5.1.4.8 interfaced to PYTHIA-6.426. Samples of Z/γ produced in association with jets are generated with SHERPA-1.4.1 [50], while ALPGEN-2.14 [51] samples are used for evaluation of systematic uncertainties. Diboson samples (W W , W Z, ZZ) are generated with POWHEG-1.0. Additional samples generated with SHERPA-1.4.1 are used to estimate the systematic arising from choice of event generator. Higgs boson production, including all decay modes, 3 is simulated with PYTHIA-8.165 [52]. Samples generated with MC@NLO-4.06, POWHEG-1.0 and SHERPA-1.4.1 are produced using the parton distribution function (PDF) set CT10 [53]. All other samples are generated using the PDF set CTEQ6L1.
The background predictions are normalised to the theoretical cross-sections, including higher-order QCD corrections where available, or are normalised to data in dedicated control regions (CRs). The inclusive cross-section for Z/γ * +jets is calculated with DYNNLO [54] with the MSTW 2008 NNLO PDF set [55]. The tt cross-section for pp collisions at a centreof-mass energy of √ s = 8 TeV is σ tt = 253 +13 −15 pb for a top-quark mass of 172.5 GeV. It has been calculated at next-to-next-to-leading order (NNLO) in QCD including resummation of next-to-next-to-leading-logarithmic (NNLL) soft gluon terms with top++2.0 [56][57][58][59][60][61]. The uncertainties due to the choice of PDF set and α s were calculated using the PDF4LHC prescription [62] with the MSTW2008 NNLO [55,63], CT10 NNLO [64,65] and NNPDF2.3 5f FFN [66] PDF sets, and were added in quadrature to the uncertainty due to the choice of renormalisation and factorisation scale. The approximate NNLO+NNLL cross-section is used for the normalisation of the W t [67] sample. The cross-sections calculated at NLO are used for the diboson [68], ttW and ttZ [69] samples.
The data sample used was recorded between March and December 2012 with the LHC operating at a pp centre-of-mass energy of √ s = 8 TeV. Data were collected based on the decision of a three-level trigger system. The events accepted passed either a single-electron, a single-muon, a double-electron, a double-muon, or an electron-muon trigger. The trigger efficiencies are approximately 99%, 96% and 91% for the events passing the full ee, eµ and µµ selections described below, respectively. After beam, detector and data-quality requirements, data corresponding to a total integrated luminosity of 20.3 fb −1 were analysed [70].

Physics object selection
Multiple vertex candidates from the proton-proton interaction are reconstructed using the tracks in the inner detector. The vertex with the highest scalar sum of the transverse momentum squared, Σp 2 T , of the associated tracks is defined as the primary vertex. Jets are reconstructed from three-dimensional energy clusters [71] in the calorimeter using the anti-k t jet clustering algorithm [72,73] with a radius parameter of 0.4. The cluster energy is corrected using calibration factors based on MC simulation and validated with extensive test-beam and collision-data studies [74], in order to take into account effects such as noncompensation and inhomogeneities, the presence of dead material and out-of-cluster energy deposits. Corrections for converting to the jet energy scale and for in-time and out-of-time pile-up are also applied, as described in Ref. [75]. Jet candidates with transverse momentum (p T ) greater than 20 GeV, |η| < 2.5 and a "jet vertex fraction" larger than 0.5 for those with p T < 50 GeV, are selected as jets in the analysis. The jet vertex fraction quantifies the fraction of the total jet momentum of the event that originates from the reconstructed primary vertex. This requirement rejects jets originating from additional proton-proton interactions.
-5 -Events containing jets that are likely to have arisen from detector noise or cosmic rays are also removed using the procedures described in ref. [76].
A neural-network-based algorithm is used to identify which of the selected jet candidates contain a b-hadron decay (b-jets). The inputs to this algorithm are the impact parameter of inner detector tracks, secondary vertex reconstruction and the topology of b-and c-hadron decays inside a jet [77]. The efficiency for tagging b-jets in an MC sample of tt events using this algorithm is 70% with rejection factors of 137 and 5 against light quarks and c-quarks, respectively. To compensate for differences between the b-tagging efficiencies and mis-tag rates in data and MC simulation, correction factors derived using tt events are applied to the jets in the simulation as described in ref. [78].
Electron candidates are required to have p T > 10 GeV, |η| < 2.47 and to satisfy "medium" electromagnetic shower shape and track selection quality criteria [79]. These are defined as preselected electrons. Signal electrons are then required to satisfy "tight" quality criteria [79]. They are also required to be isolated within the tracking volume: the scalar sum, Σp T , of the p T of inner detector tracks with p T > 1 GeV, not including the electron track, within a cone of radius ∆R = (∆η) 2 + (∆φ) 2 = 0.2 around the electron candidate must be less than 10% of the electron p T , where ∆η and ∆φ are the separations in η and φ.
Muon candidates are reconstructed either from muon segments matched to inner detector tracks, or from combined tracks in the inner detector and muon spectrometer [80]. They are required to have p T > 10 GeV and |η| < 2.4. Their longitudinal and transverse impact parameters must be within 1 mm and 0.2 mm of the primary vertex, respectively. Such preselected candidates are then required to have Σp T < 1.8 GeV, where Σp T is defined in analogy to the electron case. Event-level weights are applied to MC events to correct for differing lepton reconstruction and identification efficiencies between the simulation and those measured in data.
Ambiguities exist in the reconstruction of electrons and jets as they use the same calorimeter energy clusters as input: thus any jet whose axis lies within ∆R = 0.2 of a preselected electron is discarded. Moreover, preselected electrons or muons within ∆R = 0.4 of any remaining jets are rejected to discard leptons from the decay of a b-or c-hadron.
E miss T is defined as the magnitude of the two-vector p miss T obtained from the negative vector sum of the transverse momenta of all reconstructed electrons, jets and muons, and calorimeter energy clusters not associated with any objects. Clusters associated with electrons with p T > 10 GeV, and those associated with jets with p T > 20 GeV make use of the electron and jet calibrations of these respective objects. For jets the calibration includes the pile-up correction described above whilst the jet vertex fraction requirement is not applied. Clusters of calorimeter cells with |η| < 2.5 not associated with these objects are calibrated using both calorimeter and tracker information [81].

Preselection and event variables
A common set of preselection requirements, and some discriminating variables are shared by the three analysis strategies. The following event-level variables are defined, and their use in the various analyses is detailed in sections 5.2, 5.3 and 5.4: -m : the invariant mass of the two oppositely charged leptons.
-m T2 and m b−jet T2 : lepton-based and jet-based stransverse mass. The stransverse mass [82,83] is a kinematic variable that can be used to measure the masses of pair-produced semi-invisibly decaying heavy particles. This quantity is defined as where m T indicates the transverse mass, 4 p T,1 and p T,2 are the transverse momentum vectors of two particles (assumed to be massless), and q T,1 and q T,2 are vectors and q T = q T,1 + q T,2 . The minimisation is performed over all the possible decompositions of q T . For tt or W W decays, if the transverse momenta of the two leptons in each event are taken as p T,1 and p T,2 , and E miss T as q T , m T2 ( , , E miss T ) is bounded sharply from above by the mass of the W boson [84,85]. In thet 1 → b +χ ± 1 decay mode the upper bound is strongly correlated with the mass difference between the chargino and the lightest neutralino. If the transverse momenta of the two reconstructed bquarks in the event are taken as p T,1 and p T,2 , and the lepton transverse momenta are added vectorially to the missing transverse momentum in the event to form q T , the resulting m T2 (b, b, + + E miss T ) has a very different kinematic limit: for top-quark pair production it is approximately bound by the mass of the top quark, whilst for topsquark decays the bound is strongly correlated to the mass difference between the top squark and the chargino. In this paper, m T2 ( , , E miss T ) is referred to simply as m T2 , whilst m T2 (b, b, + + E miss T ) is referred to as m b−jet T2 . The mass of the q T is always set to zero in the calculation of these stransverse variables.
-∆φ j : the azimuthal angular distance between the p miss T vector and the direction of the closest jet.
-∆φ : the azimuthal angular distance between the p miss T vector and the direction of the highest-p T lepton.
-∆φ b and p Tb : the azimuthal angular distance between the p miss T vector and the p Tb = p miss T + p 1 T + p 2 T vector 5 . The p Tb variable, with magnitude p Tb , is the opposite of the vector sum of all the transverse hadronic activity in the event. 4 The transverse mass is defined by the equation mT = 2|pT,1||pT,2|(1 − cos(∆φ)), where ∆φ is the angle between the particles with transverse momenta pT,1 and pT,2 in the plane perpendicular to the beam axis. 5 Note that the b in p Tb (and consequently ∆φ b ) does not bear any relation to b-jet. In Ref. [86] it was so named to indicate that it represents the transverse momentum of boosted objects.
-7 --m eff : the scalar sum of the E miss T , the transverse momenta of the two leptons and that of the two jets with the largest p T in each event.
-∆φ j : the azimuthal angular distance between the highest-p T jet and lepton.
The three different analyses are referred to in this paper as the "leptonic m T2 ", "hadronic m T2 " and "multivariate analysis (MVA)", respectively. The first two are so named as they use, in the first case, m T2 , and in the second case, m b−jet T2 , as the key discriminating variable. The m T2 selection is used to ensure orthogonality between these two analyses, allowing for their results to be combined. The third uses an MVA technique and targets the on-shell top t 1 → t +χ 0 1 decay. In all cases, events are required to have exactly two oppositely charged signal leptons (electrons, muons or one of each). At least one of these electrons or muons must have p T > 25 GeV, in order for the event to be triggered with high efficiency, and m > 20 GeV (regardless of the flavours of the leptons in the pair), in order to remove leptons from low mass resonances. 6 If the event contains a third preselected electron or muon, the event is rejected. This has a negligible impact on signal acceptance, whilst simplifying the estimate of the fake and non-prompt lepton background (defined in section 6.2) and reducing diboson backgrounds.
All three analyses consider events with both different-flavour (DF) and same-flavour (SF) lepton pairs. These two event populations are separately used to train the MVA decision 7 and are explicitly separated when defining the signal regions (SRs). The decayt 1 → b +χ ± 1 is symmetric in flavour and the Z/γ * background is small, hence the populations are therefore not separated in the hadronic and leptonic m T2 analyses. All three analyses exploit the differences between the DF and SF populations when evaluating and validating background estimates.

Leptonic m T2 selection
After applying the preselection described in section 5.1, events with SF leptons are required to have the invariant mass of the lepton pairs outside the 71-111 GeV range. This is done in order to reduce the number of background events containing two leptons produced by the decay of a Z boson. Two additional selections are applied to reduce the number of background events with high m T2 arising from events with large E miss T due to mismeasured jets: ∆φ b < 1.5 and ∆φ j > 1. After these selections the background is dominated by tt events for DF lepton pairs and Z/γ +jets for SF lepton pairs. The m T2 distribution for Z/γ +jets is, however, 6 The m requirement also resolves overlap ambiguities between electron and muon candidates by implicitly removing events with close-by electrons and muons. 7 MVA uses events which are known to belong to signal or background to determine the mapping function from which it is possible to subsequently classify any given event into one of these two categories. This "learning" phase is usually called "training".
-8 -steeply falling and by requiring m T2 > 40 GeV the tt becomes the dominant background in the SF sample as well.
The leptonic m T2 selection has been optimised to target models with ∆m(χ ± 1 ,χ 0 1 ) > m(W ) ( figure 1 (a)). The jet p T spectrum is exploited in order to provide sensitivity to models with varying jet multiplicity. Four non-exclusive SRs are defined, with different selections on m T2 and on the transverse momentum of the two leading jets, as reported in table 1. The SRs L90 and L120 require m T2 > 90 GeV and m T2 > 120 GeV, respectively, with no additional requirement on jets. They provide sensitivity to scenarios with a small ∆m(t 1 ,χ ± 1 ) (almost degenerate top squark and chargino), where the production of high-p T jets is not expected. The SR L100 has a tight jet selection, requiring at least two jets with p T > 100 GeV and p T > 50 GeV, respectively, and m T2 > 100 GeV. This SR provides sensitivity to scenarios with both large ∆m(t 1 ,χ ± 1 ) and ∆m(χ ± 1 ,χ 0 1 ), where large means bigger than the W boson mass. SR L110 has a looser selection on jets, requiring two jets with p T > 20 GeV each and m T2 > 110 GeV. It provides sensitivity to scenarios with small to moderate (up to around the W boson mass) values of ∆m(t 1 ,χ ± 1 ) resulting in moderate jet activity.

Hadronic m T2 selection
In contrast to the leptonic m T2 selection, the hadronic m T2 selection is designed to be sensitive to the models with chargino-neutralino mass differences smaller than the W mass ( figure 1 (b)). In addition to the preselection described in section 5.1, events in the SR (indicated as H160) are required to satisfy the requirements given in table 2. The requirement of two b-jets favours signal over background; the targeted signal events have in general higher-p T b-jets as a result of a large ∆m(t 1 ,χ ± 1 ) ( figure 1 (b)). The tt background is then further reduced by the m b−jet T2 requirement, which preferentially selects signal models with -9 -large ∆m(t 1 ,χ ± 1 ) over the SM background. The requirement on leading lepton p T has little impact on the signal, but reduces the remaining Z/γ * +jets background to a negligible level. Table 2. Signal region used in the hadronic m T2 analysis. The last two rows give the relative sizes of the mass splittings that the SR is sensitive to: small (almost degenerate), moderate (up to around the W boson mass) or large (bigger than the W boson mass).

Multivariate analysis
In this analysis,t 1 → t +χ 0 1 signal events are separated from SM backgrounds using an MVA technique based on boosted decision trees (BDT) that uses a gradient-boosting algorithm (BDTG) [87]. In addition to the preselection described in section 5.1, events are required to have at least two jets, a leading jet with p T > 50 GeV and m eff > 300 GeV. The selected events are first divided into four (non-exclusive) categories, with the requirements in each category designed to target differentt 1 andχ E miss T , m , m T2 , ∆φ , ∆θ , ∆φ l and ∆φ j . These variables are well modelled by the simulation and are effective in discriminating t +χ 0 1 signal from SM background; the distributions in data and MC simulation for the four "best ranked" (their correlation with the BDTG ranges from ∼ 80% to ∼ 95%) input variables for the SF and DF channels after C1 cuts are shown in figures 2 and 3, respectively. In each of the sub-figures, the uncertainty band represents the total uncertainty, from all statistical and systematic uncertainty sources (section 7). The correlation coefficient between each pair of variables is found to be in good agreement (within 1-2%) between data and MC. , ∆φ j and m after C1 cuts (E miss T > 50 GeV). The contributions from all SM backgrounds are shown as a histogram stack; the bands represent the total uncertainty from statistical and systematic sources. The components labelled "Reducible" correspond to the fake and non-prompt lepton backgrounds and are estimated from data as described in section 6.2; the other backgrounds are estimated from MC simulation.
Several BDTGs are trained using the simulated SM background against one or more representative signal samples, chosen appropriately for each of the five subcategories. The BDTG training parameters are chosen to best discriminate signal events from the background, with--11 -  , ∆φ j and ∆φ after C1 cuts. The contributions from all SM backgrounds are shown as a histogram stack; the bands represent the total uncertainty from statistical and systematic sources. The components labelled "Reducible" correspond to the fake and non-prompt lepton backgrounds and are estimated from data as described in section 6.2; the other backgrounds are estimated from MC simulation. out being overtrained (MC sub-samples, which are statistically independent to the training sample, are used to check that the results are reproducible). The resulting discriminants are bound between −1 and 1. The value of the cut on each of these discriminants is chosen to maximise sensitivity to the signal points considered, with the possible values of the BDTG threshold scanned in steps of 0.01. A total of nine BDTGs (five for DF events, four for SF events) and BDTG requirements are defined, setting the SRs. They are summarised in table 3.
-12 - Table 3. Signal regions for the MVA analysis. The first column gives the name of each SR, where DF and SF indicate different and same flavours, respectively. The second column gives the signal sample used to train the BDTG. The third column lists the selection requirements applied in addition to the BDTG requirement given in the fourth column and the common SR requirements: ≥ 2 jets, leading jet p T > 50 GeV, m eff > 300 GeV.

SR
Training -13 -All backgrounds containing prompt leptons from W , Z or H decay are estimated directly from MC simulation. The dominant backgrounds (top-quark pair production for all analyses, and diboson and W t single-top production for the leptonic m T2 and hadronic m T2 analyses respectively) are normalised to data in dedicated CRs, and then extrapolated to the SRs using the MC simulation (with a likelihood fit as described in section 6.1). Whilst it is not a dominant background, Z/γ * +jets is also normalised in a dedicated CR in the hadronic m T2 analysis. All other such contributions are normalised to their theoretical cross-sections.
The backgrounds due to non-prompt leptons (from heavy-flavour decays or photon conversions) or jets misidentified as leptons are estimated using a data-driven technique. Events with these types of lepton are referred to as "fake and non-prompt" lepton events. The estimation procedure is common to all three analyses and is described in section 6.2.

Background fit
The observed numbers of events in the CRs are used to derive SM background estimates in each SR via a profile likelihood fit [88]. This procedure takes into account the correlations across the CRs due to common systematic uncertainties and the cross-contamination in each CR from other SM processes. The fit takes as input, for each SR: 1. The number of events observed in each CR and the corresponding number of events predicted in each by the MC simulation for each (non-fake, prompt) background source.
2. The number of events predicted by the MC simulation for each (non-fake, prompt) background source.
3. The number of fake and non-prompt lepton events in each region (CRs and SR) obtained with the data-driven technique (see section 6.2).
Each uncertainty source, as detailed in section 7, is treated as a nuisance parameter in the fit, constrained with a Gaussian function taking into account the correlations between sample estimates. The likelihood function is the product of Poisson probability functions describing the observed and expected number of events in the control regions and the Gaussian constraints on the nuisance parameters. For each analysis, and each SR, the free parameters of the fit are the overall normalisations of the CR-constrained backgrounds: tt, W W and (W Z, ZZ) for the leptonic m T2 analysis; tt, W t and Z/γ * +jets for the hadronic m T2 analysis and tt for the MVA analysis. The contributions from all other non-constrained prompt-lepton processes are set to the MC expectation, but are allowed to vary within their respective uncertainties. The contribution from fake and non-prompt lepton events is also set to its estimated yield and allowed to vary within its uncertainty. The fitting procedure maximises this likelihood by adjusting the free parameters; the fit constrains only the background normalisations, while the systematic uncertainties are left unchanged (i.e. the nuisance parameters always have a -14 -central value very close to zero with an error close to one). Background fit results are crosschecked in validation regions (VRs) located between, and orthogonal to, the control and signal regions. Sections 6.3 to 6.5 describe the CR defined for each analysis and, in addition, any VRs defined to cross-check the background fit results.

Fake and non-prompt lepton background estimation
The fake and non-prompt lepton background arises from semi-leptonic tt, s-channel and t-channel single-top, W +jets and light-and heavy-flavour jet production. The main contributing source in a given region depends on the topology of the events: low-m T2 regions are expected to be dominated by the multijet background, while regions with moderate/high m T2 are expected to be dominated by the W +jets and tt production. The fake and non-prompt lepton background rate is estimated for each analysis from data using a matrix method estimation, similar to that described in refs. [89,90]. In order to use the matrix method, two types of lepton identification criteria are defined: tight, corresponding to the full set of identification criteria described above, and loose, corresponding to preselected electrons and muons. The number of events containing fake leptons in each region is obtained by acting on a vector of observed (loose, tight) counts with a 4 × 4 matrix with terms containing probabilities (f and r) that relate real-real, real-fake, fake-real and fake-fake lepton event counts to tight-tight, tight-loose, loose-tight and loose-loose counts.
The two probabilities used in the prediction are defined as follows: r is the probability for real leptons satisfying the loose selection criteria to also pass the tight selection and f is the equivalent probability for fake and non-prompt leptons. The probability r is measured using a Z → ( = e, µ) sample, while the probability f is measured from two background-enriched control samples. The first of these requires exactly one lepton with p T > 25 GeV, at least one jet, E miss T < 25 GeV, and an angular distance ∆R < 0.5 between the leading jet and the lepton, in order to enhance the contribution from the multijet background. The probability is parameterised as a function of the lepton η and p T and the number of jets. For leptons with p T < 25 GeV, in order to avoid trigger biases, a second control sample which selects events containing a same-charge DF lepton pair is used. The probability f is parameterised as a function of lepton p T and η, the number of jets, m eff and m T2 . The last two variables help to isolate the contributions expected to dominate from multijet, W +jets or tt productions. In both control samples, the probability is parameterised by the number of b-jets when a b-jet is explicitly required in the event selection (i.e. in the hadronic m T2 ), in order to enhance the contribution from heavy-flavour jet production.
Many sources of systematic uncertainty are considered when evaluating this background. Like the probabilities themselves, the systematic uncertainties are also parameterised as a function of the lepton and event variables discussed above. The parameterised uncertainties are in general dominated by differences in the measurement of the fake lepton probabilities obtained when using the two control regions above. The limited number of events in the CR used to measure the probabilities are also considered as a source of systematic uncertainty. The overall systematic uncertainty ranges between 10% and 50% across the various regions -15 -(control, validation and signal). Ultimately, in SRs with very low predicted event yields the overall uncertainty on the fake and non-prompt lepton background yield is dominated by the statistical uncertainty arising from the limited number of data events in the SRs, which reaches 60-80% in the less populated SRs. In these regions, however, the contributions from fake and non-prompt lepton events are small or negligible.
The predictions obtained using this method are validated in events with same-charge lepton pairs. As an example, figure 4 shows the distribution of m eff and m T2 in events with a same-charge lepton pair after the preselection described in section 5.1, prior to any additional selection.

Leptonic m T2 analysis
The dominant SM background contributions in the SRs are tt and W W decays. Other diboson processes also expected to contribute significantly are: W Z in its 3-lepton decay mode and ZZ decaying to two leptons and two neutrinos. A single dedicated CR is defined for each of these backgrounds (CRX L , where X=T,W,Z for the tt, W W and other diboson productions respectively). Predictions in all SRs make use of the three common CRs. This choice was optimised considering the background purity and the available sample size.
The validity of the combined background estimate is tested using a set of four validation regions (VR X L , where X describes the specific selection under validation). The definitions of the CRs and VRs are given in table 4. The validity of the tt background prediction for different jet selections is checked in VR 100 L and VR 110 L . Additional SM processes yielding two isolated leptons and large E miss T (Higgs, W t, Z/γ * → +jets and ttV ) and providing a sub-dominant contribution to the SRs are determined from MC simulation. The fake and non-prompt lepton background is a small contribution (less than 10% of the total background). The composition before and after the likelihood fit is given in table 5 for the CRs and table 6 for the VRs. In these (and all subsequent) composition tables the quoted uncertainty includes all the sources of statistical and systematic uncertainty considered (see section 7.). The purity of the CRs is improved by exploiting flavour information and selecting either DF or SF pairs depending on the process being considered. The normalisation factors derived are, however, applied to all the events in a given process (both DF and SF). Checks were performed to demonstrate that the normalisation factors are not flavour-dependent. Good agreement is found between data and the SM prediction before and after the fit, leading to normalisation factors compatible with unity. The normalisations of the tt, W W and W Z, ZZ backgrounds as obtained from the fit are 0.91 ± 0.07, 1.27 ± 0.24 and 0.85 ± 0.16 respectively.
The number of expected signal events in the CRs was investigated for each signal model considered. The signal contamination in CRT L and CRW L is negligible, with the exception of signal models with top squark masses close to the top-quark mass. In this case, the signal contamination can be as high as 20% in CRT L and up to 100% in CRW L . The signal contamination in CRZ L is typically less than 10%, with a few exceptions; for signal models with top-squark masses below 250 GeV, the contamination is closer to 30%, and for signal -16 -  Figure 4. Distributions of m eff (top) and m T2 (bottom), for SF (left) and DF (right) same-charge lepton pairs, after the preselection requirements described in section 5.1. The components labelled "Reducible" correspond to the fake and non-prompt lepton backgrounds and are estimated from data as described in section 6.2. The other SM backgrounds processes which are expected to contribute events with two real leptons are shown and are estimated from MC simulation. The reconstructed leptons are required to match with a generator-level lepton in order to avoid any double counting of the total fake and non-prompt lepton contribution. The bands represent the total uncertainty. models with small ∆m(t 1 ,χ ± 1 ) the signal contamination is as high as 100%. The same CRs can be kept also for these signal models, despite the high signal contamination, since the expected yields in the SRs would be large enough for these signal models to be excluded even in the hypothesis of null expected background. The signal contamination in the VRs can be up to ∼ 100% for signal models with top-quark-like kinematics and becomes negligible when considering models with increasing top-squark masses. Figure 5 (top) shows the p Tb distribution for DF events with 40 < m T2 < 80 GeV,    -20 - -21 -

Hadronic m T2 analysis
Top-quark pair and single-top (W t-Channel) production contribute significantly to the background event yields in the SR for this analysis. Simulation shows that 49% of background events in the SR are from top-quark pair production and 37% are from W t. The next most significant SM background contributions are those arising from fake or non-prompt leptons. The remainder of the background is composed of Z/γ * +jets and W W events. The contributions from other diboson (W Z and ZZ), ttV and Higgs processes are negligible, and are estimated using the MC simulation. The CRs are defined for the combined tt and W t process, and Z/γ * (→ ee, µµ)+jets backgrounds (the Z/γ * (→ τ τ )+jets contribution is fixed at the MC expectation). The contribution from W t in the SR is dominated by its NLO contributions (which can be interpreted as top-pair production, followed by decay of one of the top-quarks). These CRs are referred to as CRX H , where X=T,Z for the (tt, W t) and Z/γ * (→ ee, µµ)+jet backgrounds respectively. The validity of the combined estimate of the W t and tt backgrounds is tested using a validation region for the top-quark background (VRT H ). The definitions of these regions are given in table 7, and their composition before and after the likelihood fit described in section 6.1 is given in table 8. Good agreement is found between data and SM prediction before and after the fit, leading to normalisations consistent with one: 0.93 ± 0.32 for the (tt,W t) and 1.5 ± 0.5 for the Z/γ * +jets backgrounds.
The signal contamination in CRZ H is negligible, whilst in CRT H it is of order 10% (16%) for models with a 300 GeV top squark and a 150 GeV (100 GeV) chargino, for neutralino masses below 100 GeV, which the region where H160 is sensitive. The signal contamination in VRT H is much higher (∼ 30%) in the same mass-space.
> 160 > 160 > 160 Figure 6 shows the m b−jet T2 distribution for events with one b-jet (using the highest p T jet which is not a b-jet with the single b-jet in the calculation of m b−jet T2 ), m T2 < 90 GeV and leading lepton p T < 60 GeV. The events with m b-jet T2 > 160 GeV in the figure are those entering CRT H . The data are in agreement with the background expectation across the distribution. Table 8. Background fit results for the two CRs and VR region in the hadronic m T2 analysis. The nominal expectations from MC simulation are given for comparison for those backgrounds (tt, W t and Z/γ * (→ ee, µ + µ − )+jets production) which are normalised to data. Combined statistical and systematic uncertainties are given. Events with fake or non-prompt leptons are estimated with the data-driven technique described in section 6.2. The observed events and the total (constrained) background are the same in the CRs by construction; this is not the case for the VR, where the consistency between these event yields is the test of the background model. Uncertainties on the predicted background event yields are quoted as symmetric except where the negative error reaches down to zero predicted events, in which case the negative error is truncated.

Channel
CRT

Multivariate analysis
In this analysis, the dominant SM background processes are top-quark pair production and diboson production. The Z/γ * +jets contribution, relevant only for the SF channel, is strongly suppressed by the BDTG requirement. The CRs are defined for tt (table 9) in regions mutually exclusive to the SRs, using BDTG intervals much more populated with tt events, while all other SM background with two isolated leptons are small and evaluated using MC simulation. The fake and non-prompt lepton background is estimated using the method described in section 6.2. In addition to the application of all non-BDTG SR cuts, the following selections are applied in the CRs: m T2 > 90 GeV and, in SF events, m which must be less than 61 GeV or greater than 121 GeV. The composition before and after the likelihood fit is given in tables 10 and 11 for the DF and SF CRs, respectively. The corresponding CR for the DF (SF) SR labelled N is denoted CRT

DF(SF) MN
. The normalisation factors derived in each CR for tt are consistent within one standard deviation (1σ) of the normalisation factor derived for tt in the leptonic-m T2 analysis.  The signal contamination in the CRs ranges from 1.5-30% (4.8-24%) in the DF (SF) CRs, whilst the contamination in the DF (SF) VRs ranges from 0.4-20% (0.9-13%).  Table 10. Background fit results for the DF CRs in the MVA analysis. The nominal expectations from MC simulation are given for comparison for tt, which is normalised to data by the fit. Combined statistical and systematic uncertainties are given. Events with fake or non-prompt leptons are estimated with the data-driven technique described in section 6.2. The observed events and the total (constrained) background are the same in the CRs by construction. Uncertainties on the predicted background event yields are quoted as symmetric except where the negative error reaches down to zero predicted events, in which case the negative error is truncated.  (bottom). The contributions from all SM backgrounds are shown as a histogram stack. The bands represent the total uncertainty. The components labelled "Reducible" correspond to the fake and nonprompt lepton backgrounds and are estimated from data as described in section 6.2; the remaining backgrounds are estimated from MC samples normalised to the luminosity of the data. The expected distribution for the signal point which was used to train the corresponding SR is also shown on each plot (see text).  Table 13. Background fit results for the DF VRs in the MVA analysis. The nominal expectations from MC simulation are given for comparison for tt, which is normalised to data. Combined statistical and systematic uncertainties are given. Events with fake or non-prompt leptons are estimated with the data-driven technique described in section 6.2. The observed events and the total (constrained) background are the same in the CRs by construction; this is not the case for the VRs, where the consistency between these event yields is the test of the background model. Entries marked -indicate a negligible background contribution. Backgrounds which contribute negligibly to all VRs are not listed. Uncertainties on the predicted background event yields are quoted as symmetric except where the negative error reaches down to zero predicted events, in which case the negative error is truncated.   -Clusters in the calorimeter energy scale, resolution and pile-up modelling.
The uncertainties related to the contribution to E miss T from the energy scale and resolution of clusters in the calorimeter not associated to electrons, muons or jets (including low momentum (7 < p T < 20 GeV) jets), as well as the uncertainty due to the modelling of pile-up were evaluated.
b-tagging (where applicable). The b-tagging uncertainty is evaluated by varying the p T -and flavour-dependent correction factors applied to each jet in the simulation within a range that reflects the systematic uncertainty on the measured tagging efficiency and rejection rates. The relative impact of this uncertainty on the final event yield is dominated by the uncertainty on the b-tagging efficiency.
-Fake and non-prompt lepton background uncertainties. The uncertainty on the fake and non-prompt lepton background arises from the limited size of the control samples used to measure the probabilities for loose leptons to pass the tight selections, the comparison of results obtained with probabilities computed with alternative control samples, and from the number of events in the loose and tight event samples.
The remaining detector-related systematic uncertainties, such as those on lepton reconstruction efficiency and on the modelling of the trigger, are of the order of a few percent. A 2.8% uncertainty on the luminosity determination was measured using techniques similar to that of Ref. [70] from a calibration of the luminosity scale derived from beam-separation scans performed in November 2012, and it is included for all signal and background MC simulations. Various theoretical uncertainties are considered in the MC modelling of the major SM backgrounds. In the case of top-quark contributions, the predictions of MC@NLO-4.06 are compared with POWHEG interfaced to HERWIG to estimate the uncertainty due to the choice of generator, while the difference in the yields obtained from POWHEG interfaced to PYTHIA and POWHEG interfaced to HERWIG is taken as the systematic uncertainty on parton showering, and the predictions of dedicated ACERMC-3.8 samples generated with different tuning parameters are compared to give the uncertainty related to the amount of ISR/FSR. At next-to-leading order, contributions with an additional bottom quark in the final state lead to ambiguities in the distinction between the W t process (gb → W t) and topquark pair production. In the hadronic m T2 analysis this becomes significant as the SR is a region of phase space where these ambiguities are important. All the W t samples, generated using MC@NLO-4.06 and POWHEG-1.0, use the diagram removal [92] scheme. ACERMC-3.8 is used to generate a leading-order (LO) prediction of the W W b and W W bb final state (which includes both tt and W t single-top processes); the predictions of these ACERMC-3.8 samples and MC@NLO-4.06 are then compared in order to assess the uncertainty on the background estimate from this interference.
The uncertainties on diboson production are evaluated by comparing the predictions of POWHEG-1.0 and SHERPA-1.4.1, and the uncertainties on Z/γ * +jets production are evaluated by comparing the predictions of SHERPA-1.4.1 and ALPGEN-2.14. The former comparison includes the impact of choice of parton showering scheme.
The impact of the evaluated systematic uncertainties on the different SRs presented are shown in tables 15, 16 and 17. These tables quote, for each SR, the percentage of the total systematic uncertainty on the background yield which is attributed to each source. Since these uncertainties are correlated, there is no requirement for these to sum in quadrature to 100%. These correlations are particularly strong in H160, where there are strong cancellations between the tt and W t normalisation and the top-quark generator systematic uncertainties. The uncertainty on the W Z/ZZ normalisation (where appropriate) has comparable statistical and systematic components, whilst the tt (tt, W t) and W W normalisation uncertainties are dominated by systematic effects.
Systematic uncertainties are also taken into account for expected signal yields. The uncertainty on the signal cross-sections is calculated with an envelope of cross-section predictions which is defined using the 68% CL ranges of the CTEQ [39] (including the α s uncertainty) and MSTW [55] PDF sets, together with variations of the factorisation and renormalisation scales by factors of two or one half. The nominal cross-section value is taken to be the midpoint of the envelope and the uncertainty assigned is half the full width of the envelope, using the procedure described in ref. [43]. The typical cross-section uncertainty is 15% for the top-squark signal. Uncertainties on signal shape related to the generation of the SUSY samples are determined using additional samples with modified parameters. This includes uncertainties on the modelling of ISR and FSR, the choice of renormalisation/factorisation scales, and the parton-shower matching scale settings. These uncertainties are relevant only in the case of small ∆m(t 1 ,χ ± 1 ) for thet 1 → b+χ ± 1 decay mode or when m(t 1 ) m(t)+m(χ 0 1 ) for thet 1 → t +χ 0 1 decay mode. They have an impact of up to 10% (20%) on the acceptance in thet 1 → b +χ ± 1 (t 1 → b +χ 0 1 ) case depending on the SR, but yield negligible effects on

Results and interpretation
Tables 18 to 21 report the background yields (before and after the background-only likelihood fit) and the observed numbers of events in the various SRs. In each, agreement is found between the SM prediction and the data, within uncertainties. In all tables the quoted uncertainty includes all the sources of statistical and systematic uncertainty considered (see section 7). The agreement between the SM prediction and the data is tested separately for the SF and DF populations in L90 (the SR with the highest predicted background yield) as an additional check. Results of this check are consistent with the inclusive result in both the SF (123 observed and 136 ± 19 expected events) and DF (151 observed and 164 ± 31 expected events) samples, with the background composition being dominated by the flavour symmetric -32 - tt and W W backgrounds. Small differences in the background composition arise from the W Z and ZZ backgrounds, which account for 8% of the total background SF events and < 1% of the total background DF events. Other minor differences are a result of the fake and non-prompt lepton background which accounts for 6% of the DF background but only 2% of the SF background. Zγ * → events contribute only to the SF channel, and are 2% of the total background event yield. Figures 8 to 10 illustrate the distribution of m T2 in the different SRs of the leptonic m T2 analysis, prior to any cut on m T2 , after the background fit. In this figure, the events are separated into DF and SF lepton pairs, illustrating the similarity of the background composition between the two populations (and the negligible size of Z/γ * +jets in the SRs themselves). Figure 11 illustrates the distribution of m b−jet T2 in SR H160, prior to any cut on m b−jet T2 , after the background fit. Figure 12 illustrates the BDTG distribution, prior to any cut on BDTG and after the background fit, for the DF and SF channels of the MVA analysis as obtained from the trainings which used the point (m(t), m(χ 0 1 )) = (300, 50) GeV and (m(t),m(χ 0 1 )) = (300, 100) GeV, respectively.
-33 -  Cluster energy scale  21  23  23  15  and resolution  Pile-up  21  32  21  14  Diboson generator  6  13  5  2  Top-quark generator  71  50  42  26  Top-quark decay: ISR/FSR  25  24  12  17  Top-quark decay: parton shower  16  14  21  13  Simulation statistics  48  38  44  37  Fake and non-prompt leptons  19  38  36  6  tt normalisation  75  55  27  37 -34 - Expected Higgs boson events 0.65 ± 0.22 0.02 +0.02 −0.02 0.03 ± 0.03 0.31 ± 0.12 Expected events with fake and non-prompt leptons 13.0 ± 3.5 --1.0 ± 0.6 1.1 ± 0.8 Table 19. Number of events and composition in SR H160 for an integrated luminosity of 20.3 fb −1 in the hadronic m T2 analysis. The nominal expectations from MC simulation are given for comparison for those backgrounds (tt, W t and Z/γ * (→ ee, µ + µ − )+jets production) that are normalised to data. Combined statistical and systematic uncertainties are given. Events with fake or non-prompt leptons are estimated with the data-driven technique described in section 6.2.. Uncertainties on the predicted background event yields are quoted as symmetric except where the negative error reaches down to zero predicted events, in which case the negative error is truncated. Expected ttV events 0.47 ± 0.16 Expected W Z, ZZ events 0.11 ± 0.11 Expected Z/γ * → τ τ +jets events 0.86 ± 0.15 Expected events with fake and non-prompt leptons 2.5 ± 0.4 Expected Higgs boson events 0.08 ± 0.02 Table 20. Number of events and composition of the DF signal regions for an integrated luminosity of 20.3 fb −1 in the MVA analysis. Nominal MC simulation expectation is given for comparison for the background (tt) that is normalised to data. Combined statistical and systematic uncertainties are given. Events with fake or non-prompt leptons are estimated with the data-driven technique described in section 6.3. Entries marked --indicate a negligible background contribution. Backgrounds which contribute negligibly to all SRs are not listed. Uncertainties on the predicted background event yields are quoted as symmetric except where the negative error reaches down to zero predicted events, in which case the negative error is truncated.  Table 21. Number of events and composition of the SF signal regions for an integrated luminosity of 20.3 fb −1 in the MVA analysis. Nominal MC simulation expectation is given for comparison for the background (tt) that is normalised to data. Combined statistical and systematic uncertainties are given. Events with fake or non-prompt leptons are estimated with the data-driven technique described in section 6.3. Entries marked --indicate a negligible background contribution. Backgrounds which contribute negligibly to all SRs are not listed. Uncertainties on the predicted background event yields are quoted as symmetric except where the negative error reaches down to zero predicted events, in which case the negative error is truncated.  Upper limits at 95% CL on the number of beyond-the-SM (BSM) events for each SR are derived using the CL s likelihood ratio prescription as described in ref.

Channel
[93] and neglecting any possible contamination in the control regions. Normalising these by the integrated luminosity of the data sample, they can be interpreted as upper limits on the visible BSM cross-section, σ vis = σ × × A, where σ is the production cross-section for the BSM signal, A is the acceptance defined by the fraction of events passing the geometric and kinematic selections at particle level, and is the detector reconstruction, identification and trigger efficiency (see appendix A). Table 22 summarises, for each SR, the estimated SM background yield, the observed numbers of events, and the expected and observed upper limits on event yields from a BSM signal and on σ vis . The results obtained are used to derive limits on the mass of a pair-produced top squark t 1 decaying with 100% BR into the lightest chargino and a b-quark (for the leptonic and hadronic m T2 analyses), an off-shell t-quark and the lightest neutralino (for the leptonic m T2 analyses) or an on-shell top quark and the lightest neutralino (for the MVA).
The inclusive SRs in the leptonic m T2 analysis were designed to maximise the discovery potential of the analysis. In the absence of any excess, a set of statistically exclusive SR can be defined in order to maximise the exclusion power of the search. Thus, in order to -43 -allow a statistical combination of the leptonic m T2 SRs and maximise this potential, a set of seven statistically independent SRs is defined in the (jet selections, m T2 ) plane, as shown in figure 13. These SRs are labelled Sn, with n ranging from one to seven. Table 23 reports the background yields (after the likelihood fit) and upper limits on the visible cross-sections for each of these SRs. In each, agreement is found between the SM prediction and the data. A fit similar to that described in section 6.1 is used to evaluate exclusion contours in various two-dimensional mass parameter planes. In this fit, the CRs and SR(s) are fit simultaneously taking into account the experimental and theoretical systematic uncertainties as nuisance parameters. The signal contamination of the CRs is taken into account in the fit. The fit thus differs from the "background-only" fit described in section 6.1 as follows: 1. An extra free parameter for a possible BSM signal strength which is constrained to be non-negative is added.
2. The number of events observed in the signal region is now also considered as an input to the fit.
3. The expected contamination of the control regions by the signal is included in the fit.
Systematic uncertainties on the signal expectations stemming from detector effects are included in the fit in the same way as for the backgrounds. Systematic uncertainties on the signal cross-section due to the choice of renormalisation and factorisation scale and PDF uncertainties are calculated as described earlier but not included directly in the fit. In all resulting exclusion contours the dashed (black) and solid (red) lines show the 95% CL expected and observed limits, respectively, including all uncertainties except for the theoretical signal cross-section uncertainty (PDF and scale). The (yellow) bands around the expected limits show the ±1σ expectations. The dotted ±1σ (red) lines around the observed limit represent the results obtained when moving the nominal signal cross-section up or down by its theoretical uncertainty. Quoted numerical limits on the particle masses are taken from these −1σ "theory lines". For the leptonic and hadronic m T2 analyses, various two-dimensional slices in the threedimensional mass parameter space m(t 1 ,χ ± 1 ,χ 0 1 ) are used to quantify the exclusion contours on these parameters in thet 1 → b +χ ± 1 mode: in the (t 1 ,χ ± 1 ) mass plane for a neutralino with a mass of 1 GeV (figure 14); in the (t 1 ,χ 0 1 ) mass plane for a fixed value of m(t 1 ) − m(χ ± 1 ) = 10 GeV (figure 15); in the (χ ± 1 ,χ 0 1 ) mass plane for a fixed 300 GeV top squark (figure 16); and in the (t 1 ,χ 0 1 ) mass plane for m(χ ± 1 ) = 2m(χ 0 1 ) ( figure 17). For the above limits, in each case all the exclusive SRs of the leptonic m T2 analysis are combined when setting the exclusions. The hadronic m T2 SR, H160, is added into the combination in the plane with fixed 300 GeV top-squark mass, a projection in which the m b−jet T2 variable is expected to increase sensitivity, and for points in the 1 GeV neutralino and the m(χ ± 1 ) = 2m(χ 0 1 ) planes with m(t 1 ) = 300 GeV. In particular, in this last plane (figure 17), the contribution from the hadronic m T2 SR is the narrow corridor at m(t 1 ) = 300 GeV and low m(χ 0 1 ): this is the result of the sensitivity being limited on the higher m(t 1 ) side by the decreasingt 1 production cross-section and at lower masses by the m b-jet T2 cut acceptance. The optimal choice of m b-jet

T2
-45 -cut-value is heavily dictated by the shape and expected sharp end-point of m b-jet T2 for the tt background, rather than the end-points expected for signal events.
For the MVA analysis, the exclusion contours for an on-shell top-quark in at 1 → t +χ 0 1 decay are quantified in the m(t 1 ) − m(χ 0 1 ) plane ( figure 18), taking the best expected DF and SF SRs (defined as the regions with the lowest value of the expected CL s ), for each point, and combining them statistically.
The results of the leptonic m T2 analysis are used to derive limits on the mass of a top squark decaying with 100% BR into bWχ 0 1 ( figure 19) and the results of the hadronic m T2 analysis are also used to derive limits ont 1 → b +χ ± 1 for fixed 106 GeV chargino mass (figure 20), a grid introduced by CDF in ref.
[29].  Figure 14. Observed and expected exclusion contours at 95% CL in the (t 1 ,χ ± 1 ) mass plane for a fixed value of m(χ 0 1 ) = 1 GeV. The dashed and solid lines show the 95% CL expected and observed limits, respectively, including all uncertainties except for the theoretical signal cross-section uncertainty (PDF and scale). The band around the expected limit shows the ±1σ expectation. The dotted ±1σ lines around the observed limit represent the results obtained when moving the nominal signal cross-section up or down by the theoretical uncertainty.

Conclusions
The results of a search for the production of the lightest top squarkt 1 in a 20.3 fb −1 dataset of LHC pp collisions at √ s = 8 TeV recorded by ATLAS are reported. Events with two oppositely charged leptons (electrons or muons) were analysed and data compared to SM predictions in a variety of SRs. Results are in agreement with SM predictions across all SRs.
- 46 -The observations in the various SRs are used to produce 95% CL upper limits ont 1 pair production assuming either the decayt 1 → b +χ ± 1 or the decayt 1 → t +χ 0 1 (each with 100% BR) for different assumptions on the mass hierarchy of the top squark, chargino and lightest neutralino. In thet 1 → t +χ 0 1 case, and for an on-shell t-quark, the SRs considered utilised an MVA technique.
For the case of a 1 GeV neutralino, a top-squarkt 1 with a mass between 150 GeV and 445 GeV decaying to a b-quark and a chargino is excluded at 95% CL for a chargino approximately degenerate with the top squark. For a 300 GeV top squark decaying to a b-quark and a chargino, chargino masses between 100 GeV and 290 GeV are excluded for a lightest neutralino with mass below 70 GeV. Top squarks of masses between 215 GeV and 530 GeV decaying to an on-shell t-quark and a neutralino of mass 1 GeV are excluded at 95% CL. Limits are also set on the direct three-body decay mode,t 1 → t +χ 0 1 with an offshell t-quark (t 1 → Wχ 0 1 b), excluding a top squark between 90 GeV and 170 GeV, under the assumption of a 1 GeV neutralino.    Figure 17. Observed and expected exclusion contours at 95% CL in the (t 1 ,χ 0 1 ) mass plane for m(χ ± 1 ) = 2m(χ 0 1 ). The dashed and solid lines show the 95% CL expected and observed limits, respectively, including all uncertainties except for the theoretical signal cross-section uncertainty (PDF and scale). The band around the expected limit shows the ±1σ expectation. The dotted ±1σ lines around the observed limit represent the results obtained when moving the nominal signal cross-section up or down by the theoretical uncertainty. The solid blue area labelled 1-2L is the exclusion contour from an ATLAS search for direct top squark production in events with one or two leptons [19]. . Observed and expected exclusion contours at 95% CL in the (t 1 ,χ 0 1 ) mass plane assuming t 1 → t +χ 0 1 . The dashed and solid lines show the 95% CL expected and observed limits, respectively, including all uncertainties except for the theoretical signal cross-section uncertainty (PDF and scale). The band around the expected limit shows the ±1σ expectation. The dotted ±1σ lines around the observed limit represent the results obtained when moving the nominal signal cross-section up or down by the theoretical uncertainty.  Figure 19. Observed and expected exclusion contours at 95% CL in the (t 1 ,χ 0 1 ) mass plane assuming t 1 → bWχ 0 1 with 100% BR. The dashed and solid lines show the 95% CL expected and observed limits, respectively, including all uncertainties except for the theoretical signal cross-section uncertainty (PDF and scale). The band around the expected limit shows the ±1σ expectation. The dotted ±1σ lines around the observed limit represent the results obtained when moving the nominal signal cross-section up or down by the theoretical uncertainty. . Observed and expected exclusion contours at 95% CL in the (t 1 ,χ 0 1 ) mass plane for a fixed value of m(χ ± 1 ) = 106 GeV. The dashed and solid lines show the 95% CL expected and observed limits, respectively, including all uncertainties except for the theoretical signal cross-section uncertainty (PDF and scale). The band around the expected limit shows the ±1σ expectation. The dotted ±1σ lines around the observed limit represent the results obtained when moving the nominal signal cross-section up or down by the theoretical uncertainty. The solid green area shows the excluded region from a previous ATLAS two-lepton analysis [19]. [31] ATLAS collaboration, The ATLAS Experiment at the CERN Large Hadron Collider, JINST 3 (2008) S08003.
[32] ATLAS Collaboration, Measurement of underlying event characteristics using charged particles in pp collisions at √ s = 900 GeV and 7 TeV with the ATLAS detector in a limited phase space, ATLAS-CONF-2011-009. https://cds.cern.ch/record/1330721.  [91] ATLAS Collaboration, Jet energy resolution and reconstruction efficiencies from in-situ techniques with the ATLAS detector using proton-proton collisions at a centre-of-mass energy √ s = 7 TeV, ATL-CONF-2010-054. http://cdsweb.cern.ch/record/1281311. -59 -A Generator-level object and event selection The generator-level MC information is used to determine the acceptance and the efficiency for simulated signal events in this analysis. The acceptance is defined as the fraction of signal events which pass the analysis selection performed on generator-level objects, therefore emulating an ideal detector with perfect particle identification and no measurement resolution effects. The efficiency is the ratio between the expected signal rate calculated with simulated data passing all the reconstruction level cuts applied to reconstructed objects, and the signal rate for the ideal detector. In this section, the details of the generator-level object and event selection information are given. The input to the object selection algorithm is the particles from the generated primary proton-proton collision after parton shower and final-state radiation, and after the decay of unstable supersymmetric particles, hadrons and τ leptons. Muons and hadrons with a lifetime comparable to or larger than the time of flight through the detector are not decayed.
Jets are reconstructed using the anti-k t jet clustering algorithm with radius parameter of 0.4, as for the simulated and observed data, but the particle input to the algorithm is restricted to MC particles other than muons, neutrinos, and neutralinos. All jets which have a b-quark with p T > 5 GeV within a ∆R < 0.4 of the jet axis are considered as b-jet.
Electrons or muons are considered if they are produced by the decay of a W ,Z, or Higgs boson, a supersymmetric particle, or if they are produced by the decay of a τ lepton which was produced by the decay of these particles. The same selections on p T and η applied to reconstructed electrons, muons and jets, as well as the ∆R selections between them, described in section 4, are applied also at generator-level.
The truth E miss T is taken as the sum of momenta of weakly interacting particles (neutrinos and neutralinos).
The event selection described in section 5 is then performed on the selected electrons, muons, jets, and E miss T .