Search for direct top squark pair production in events with a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Z$$\end{document}Z boson, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b$$\end{document}b-jets and missing transverse momentum in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sqrt{s}=8$$\end{document}s=8 TeV \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$pp$$\end{document}pp collisions with the ATLAS detector

A search is presented for direct top squark pair production using events with at least two leptons including a same-flavour opposite-sign pair with invariant mass consistent with the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Z$$\end{document}Z boson mass, jets tagged as originating from \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b$$\end{document}b-quarks and missing transverse momentum. The analysis is performed with proton–proton collision data at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sqrt{s}=8{\hbox {\ TeV}}$$\end{document}s=8TeV collected with the ATLAS detector at the LHC in 2012 corresponding to an integrated luminosity of 20.3 fb\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-1}$$\end{document}-1. No excess beyond the Standard Model expectation is observed. Interpretations of the results are provided in models based on the direct pair production of the heavier top squark state (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tilde{t}_2$$\end{document}t~2) followed by the decay to the lighter top squark state (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tilde{t}_1$$\end{document}t~1) via \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tilde{t}_2 \rightarrow Z\tilde{t}_1$$\end{document}t~2→Zt~1, and for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tilde{t}_1$$\end{document}t~1 pair production in natural gauge-mediated supersymmetry breaking scenarios where the neutralino (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tilde{\chi }^0_1$$\end{document}χ~10) is the next-to-lightest supersymmetric particle and decays producing a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Z$$\end{document}Z boson and a gravitino (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tilde{G}$$\end{document}G~) via the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tilde{\chi }^0_1 \rightarrow Z\tilde{G}$$\end{document}χ~10→ZG~ process.

In a large variety of models, the LSP is the lightest neutralino (χ 0 1 ) which is a mixture of the neutral supersymmetric partners of the gauge and Higgs bosons, known as gauginos and higgsinos. Similarly, charginos are a mixture of the charged gauginos and higgsinos, with the lightest denoted byχ ± 1 . The scalar partners of right-handed and left-handed quarks,q R andq L , mix to form two mass eigenstates,q 1 and q 2 , withq 1 defined to be the lighter of the two. Naturalness e-mail: atlas.publications@cern.ch arguments [15,16] imply that the supersymmetric partners of the top quark (stops) are light, with mass below 1 TeV.
Searches for direct pair production of thet 1 have been performed by the ATLAS [17][18][19][20][21][22] and CMS [23][24][25][26] collaborations. These searches witht 1 → tχ 0 1 currently have little sensitivity to scenarios where the lightest stop is only slightly heavier than the sum of the masses of the top quark and the LSP, due to the similarities in kinematics with SM top pair production (tt). In those scenarios, by considering instead the direct pair production of the heavy stop (t 2 ) decaying viã t 2 → Zt 1 , stop signals can be discriminated from the tt background by requiring a same-flavour opposite-sign (SFOS) lepton pair originating from the Z boson decay. Requiring a third lepton, that in signal events can be produced from the top quark in thet 1 → tχ 0 1 decay, can further reject tt. Sensitivity to directt 2 pair production can be obtained with this three-lepton signature even in models where additional decay modes of thet 2 , such ast 2 → tχ 0 1 or via the lightest Higgs boson (h) int 2 → ht 1 , are significant.
A similar signature can also occur int 1 pair production in gauge-mediated SUSY breaking (GMSB) models [27][28][29][30][31][32]. Theχ 0 1 fromt 1 decay is typically the next-to-lightest supersymmetric particle (NLSP) and the supersymmetric partner of the graviton (gravitino,G) is typically the LSP and is very light (mG < 1 keV). Assuming a mass scale of the messengers responsible for the supersymmetry breaking of around 10 TeV and little fine tuning [15], the lightest stop is expected to have a mass of less than 400 GeV [33]. Theχ 0 1 decays to either a γ , Z , or h boson and aG. If theχ 0 1 is higgsino-like, as suggested by naturalness arguments, it dominantly decays either viaχ 0 1 → hG or viaχ 0 1 → ZG, in the latter case giving a Z boson at the end of the stop decay chain.
In this paper a search for stop pair production is reported in final states characterised by the presence of a Z boson with or without additional leptons, plus jets originating from b-quarks (b-jets) produced in the stop decay chain and significant missing transverse momentum from the undetected LSPs. Results are interpreted in simplified models featuring t 2 production and in the framework of natural GMSB. This paper presents the first result ont 2 direct pair production and extends the results of a previous ATLAS analysis, carried out using 7 TeV data corresponding to an integrated luminosity of 2.05 fb −1 [34], that excluded stop masses up to 310 GeV for 115 GeV < mχ0 1 < 230 GeV in natural GMSB scenarios.

The ATLAS detector
ATLAS [35] is a general-purpose particle physics experiment at the LHC. The layout of the detector consists of inner tracking devices surrounded by a superconducting solenoid, electromagnetic and hadronic calorimeters and a muon spectrometer with a magnetic field produced by three large superconducting toroids each with eight coils. The inner tracking detector is formed from silicon pixel and microstrip detectors, and a straw tube transition radiation tracker, and provides precision tracking of charged particles for pseudorapidity |η| < 2.5. 1 The calorimeter system, placed outside the solenoid, covers |η| < 4.9 and is composed of electromagnetic and hadronic sampling calorimeters with either liquid argon or scintillating tiles as the active medium. The muon spectrometer surrounds the calorimeter and consists of a system of precision tracking chambers within |η| < 2.7, and detectors for triggering within |η| < 2.4.

Signal and background simulation
Monte Carlo (MC) simulated event samples are used to aid in the estimation of the SM background and to model the SUSY signal. MC samples are processed through a detector simulation [36] based on Geant4 [37] or a fast simulation using a parameterisation of the performance of the electromagnetic and hadronic calorimeters and Geant4 for the other parts of the detector [38], and are reconstructed in the same manner as the data. The simulation includes the effect of multiple pp collisions in the same and neighbouring bunch crossings and is weighted to reproduce the observed distribution of the average number of collisions per bunch crossing. All MC samples used in the analysis are produced using the ATLAS underlying event tune 2B [39] unless otherwise stated. 1 ATLAS uses a right-handed coordinate system with its origin at the nominal pp interaction point (IP) in the center of the detector and the z-axis along the beam. 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). The separation between final state particles is defined as R = ( η) 2 + ( φ) 2 . The transverse momentum is denoted as p T .
The top-quark pair production background is simulated with Powheg Box r2129 [40][41][42] interfaced to Pythia 6.427 [43] for the fragmentation and hadronisation processes. The mass of the top quark is fixed at 172.5 GeV, and the next-to-leading order (NLO) parton distribution function (PDF) set CT10 [44] is used. The total cross section is calculated at next-to-next-to-leading-order (NNLO) including resummation of next-to-next-to-leading logarithmic (NNLL) soft gluon terms with top++2.0 [45][46][47][48][49][50]. The P2011C [51] MC tune is used for this sample. Samples generated with Alpgen 2.14 [52] interfaced with Herwig 6.510 [53], including Jimmy 4.3 [54] for the underlying event description, are used to evaluate generator systematic uncertainties, while Powheg Box r2129 interfaced to Herwig 6.510 and AcerMC 3.8 [55] interfaced to Pythia 6.426 are used for hadronisation and initial/final state radiation (ISR/FSR) uncertainty estimation respectively. Production of a single top quark in association with a W boson is simulated with Powheg Box r2129 interfaced to Pythia 6.426 using the diagram removal scheme [56]. The nominal samples describing tt production in association with gauge bosons (tt V ) as well as single top production in association with a Z boson (t Z) in the t-and s-channels, and the t W Z process, are generated using the leading-order (LO) generator MadGraph5 1.3.33 [57] interfaced to Pythia 6.426 for the fragmentation and the hadronisation. The total cross sections of tt W and tt Z are normalised to NLO [58] while t Z is normalised to the LO cross section from the generator, since NLO calculations are currently only available for the t-channel [59]. To estimate generator and hadronisation systematic uncertainties for the tt W and tt Z processes, Alpgen 2.14 interfaced with Herwig 6.520, including Jimmy 4.3, is used. Samples of Z /γ * production in association with up to five jets are produced with Sherpa 1.4.1 [60] where b-and c-quarks are treated as massive. MC samples of dibosons (Z Z, W Z and W W ) decaying to final states with 2, 3 and 4 leptons are generated using Powheg Box r2129 interfaced to Pythia 8.163 [61]. Samples generated with aMC@NLO [62] (in MadGraph5 2.0.0.beta) interfaced to Pythia 6.427 or Herwig 6.510 are used to evaluate generator, hadronisation and scale variation uncertainties. Samples of tribosons (W W W , Z W W and Z Z Z) are generated with MadGraph5 1.3.33 interfaced to Pythia 6.426 and normalised to NLO [63]. Higgs boson production in association with a vector boson or tt pair is simulated with Pythia 8.165, with cross sections calculated at NNLO QCD + NLO electroweak precision, except pp → tth, which is calculated at NLO QCD precision [64]. The multijet and γ +jet processes are simulated with Pythia 8.165 and Pythia 8.160 respectively.
Signal events are generated according to SUSY models using Herwig++ 2.5.2 [65] with the CTEQ6L1 PDF set. Signal cross sections are calculated at NLO + NLL accuracy [66][67][68]. The nominal cross section and the uncer-tainty are taken from an envelope of cross section predictions using different PDF sets and factorisation and renormalisation scales, as described in Ref. [69]. Directt 2 pair production is studied using a simplified model, where all SUSY particles are decoupled except for thet 2 ,t 1 andχ 0 1 , assumed to be the LSP. The only decays included in this model aret 2 → Zt 1 andt 1 → tχ 0 1 . The mass of the top quark is fixed at 172.5 GeV. The mass difference between the lighter stop and the neutralino is set to 180 GeV, a region not excluded by previous searches [21], and signal samples are generated varying the masses of thẽ t 2 andχ 0 1 . In addition, dedicated samples also including thẽ t 2 → ht 1 andt 2 → tχ 0 1 decay modes are used to interpret the results as a function of thet 2 branching ratios. Simulated samples corresponding to directt 1 pair production for values of mt 1 = mχ0 1 + 180 GeV are also used in the analysis. For the natural GMSB scenario, a very similar model to that of Ref. [34] is considered, with the Higgs boson assumed to be SM-like and with the mass set at 126 GeV, in agreement with the observation of a Higgs boson at the LHC [70,71], and with tan β, the ratio of the vacuum expectation value of the two neutral Higgs doublets of the MSSM, set to 5. The masses of the first and second generation squarks and gluinos (superpartners of the gluons) are above 5 TeV, and maximal mixing between the squark eigenstates is assumed fort 1 . Onlyt 1 pair production is considered.χ 0 1 ,χ 0 2 andχ ± 1 are assumed to be predominantly higgsino states. Hence, ifχ 0 2 or χ ± 1 are produced in a decay chain, they decay toχ 0 1 promptly with soft accompanying fermions. The branching fractions of thet 1 and higgsino decays are predicted by the model. If mt 1 < m t + mχ0 1 ,t 1 decays viat 1 → bχ ± 1 exclusively, while if mt 1 > m t +mχ0 1 ,t 1 may also decay with similar probability viat 1 → tχ 0 1 (or tχ 0 2 ). For the model parameters considered, theχ 0 1 predominantly decays to ZG with branching ratios typically above 70 %. Signal samples are generated varying thet 1 andχ 0 1 masses.

Object identification and event selection
After the application of beam, detector and data quality requirements, the total luminosity considered in this analysis corresponds to 20.3 fb −1 . The uncertainty on the integrated luminosity is ±2.8 %. It is derived, following the same methodology as that detailed in Ref. [72], from a preliminary calibration of the luminosity scale derived from beamseparation scans performed in November 2012. Events are selected if they pass the single electron or muon triggers; these are fully efficient for lepton p T > 25 GeV. The presence of at least one primary vertex, with at least five tracks with p T > 0.4 GeV associated to it, is required. In order to optimize the analysis and to perform data-driven background estimations, two categories of jets, electrons, muons and photons are defined: "candidate" and "signal" (with tighter selection criteria).
Jets are reconstructed from three-dimensional calorimeter energy clusters by using the anti-k t algorithm [73] with a radius parameter of 0.4. Jet energies are corrected [74] for detector inhomogeneities, the non-compensating nature of the calorimeter, and the impact of multiple overlapping pp interactions, using factors derived from test beam, cosmic ray and pp collision data and from a detailed Geant4 detector simulation. Events with any jet that fails the jet quality criteria designed to remove noise and non-collision backgrounds [74] are rejected. Jet candidates are required to have p T > 20 GeV and |η| < 2.8. Jets labelled as signal jets are further required to have p T > 30 GeV and, for those with p T < 50 GeV and |η| < 2.4, the jet vertex fraction, defined as the fraction of the sum of the p T of the tracks associated with the jet and matched to the selected primary vertex, normalised by the sum of the p T of all tracks associated with the jet, is required to be larger than 25 %.
Identification of jets containing b-quarks (b-tagging) is performed with a dedicated algorithm based on a neuralnetwork approach which uses the output weights of several b-tagging algorithms [75] as input. A requirement is chosen corresponding to a 60 % average efficiency obtained for b-jets in simulated tt events. The rejection factors for mis-tagging light quark jets, c-quark jets and τ leptons in simulated SM tt events are approximately 600, 8 and 24, respectively. Signal jets with |η| < 2.5 which satisfy this b-tagging requirement are identified as b-jets. To compensate for differences between data and MC simulation in the b-tagging efficiencies and mis-tag rates, correction factors derived from different methods, such as the use of the p T of muons relative to the axis of the jet [76] and a dedicated study in tt dominated regions [77], are applied to the simulated samples. A sample of D * + mesons is used for mis-tag rates of c-jets [78] and inclusive jet samples for mis-tag rates of a jet which does not originate from a b-or c-quark [79].
Electron candidates must satisfy the "medium" selection criteria described in Ref. [80], re-optimised for 2012 data, and are required to fulfil p T > 10 GeV and |η| < 2.47. Signal electrons must pass the previous requirements and also need to be isolated, i.e. the scalar sum of the p T of charged-particle tracks within a cone of radius R = 0.3 around the candidate excluding its own track must be less than 16 % of the electron p T . In addition, a longitudinal impact parameter requirement of |z 0 sin θ | < 0.4 mm is applied to signal electrons. The track parameter z 0 is defined with respect to the reconstructed primary vertex.
Muon candidates are required to have p T > 10 GeV, |η| < 2.4 and are identified by matching an extrapolated inner detector track and one or more track segments in the muon spectrometer [81]. Signal muons are then required to be isolated, i.e. the scalar sum of the p T of charged-particle tracks within a cone of radius R = 0.3 around the muon candidate excluding its own track must be less than 12 % of the muon p T . In addition, a longitudinal impact parameter requirement of |z 0 sin θ | < 0.4 mm is applied to signal muons.
A signal lepton with p T larger than 25 GeV is required to match the one that triggered the event such that the efficiency of the trigger is p T independent. The MC events are corrected to account for minor differences in the lepton trigger, reconstruction and identification efficiencies between data and MC simulation [80,81].
To resolve ambiguities between reconstructed jets and leptons, jet candidates within a distance of R = 0.2 of an electron candidate are rejected. Any electron or muon candidate within a distance of R = 0.4 of any remaining jet candidate is also rejected. To suppress the rare case where two distinct tracks are mistakenly associated with one calorimeter energy cluster forming two electron candidates, if two electron candidates are found within a distance R = 0.1, the one with smaller transverse momentum is rejected. Finally, to suppress muon bremsstrahlung leading to an incorrect measurement of the transverse momentum, if an electron candidate and a muon candidate are within R = 0.1, both are rejected.
Photons are used only for the Z +jets estimation in the two-lepton signal regions described in Sect. 5 and the overlap removal between photons and jets described below is performed only in this case. Photon candidates are required to have p T > 25 GeV, |η| < 2.47 and must satisfy the "tight" selection criteria described in Ref. [82]. Signal photons are further required to be isolated, i.e. the scalar sum of transverse energy deposition in the calorimeter observed within a cone of radius R = 0.4 around the photon candidate excluding its own energy deposition in the calorimeter must be less than 4 GeV. To resolve overlaps between reconstructed jets and photons, jet candidates within a distance of R = 0.2 of a photon candidate are rejected.
The calculation of the missing transverse momentum, where its magnitude is referred to as E miss T [83], is based on the vector sum of the transverse momenta of all electron, muon and jet candidates, as well as photons with p T > 10 GeV and calibrated calorimeter energy clusters with |η| < 4.9 not associated with these objects. Clusters associated with electrons, photons and jets make use of the calibrations of these objects. For jets, the calibration includes the pile-up correction described above, whilst the jet vertex fraction requirement is not considered when selecting jet candidates for computing the E miss T . Clusters not associated with these objects are calibrated using both calorimeter and tracker information [83].
Five signal regions (SRs) are defined in the analysis aiming at final states with a Z boson, b-jets, significant E miss T and possibly additional leptons, as summarised in Table 1. They are characterised by the number of leptons (electrons or muons) required in the final state. For the two-lepton SRs (indicated as SR2A, SR2B and SR2C), events with exactly two leptons are selected, with the p T of the leading one required to be larger than 25 GeV. They are required to be signal leptons and form a SFOS pair with invariant mass (m ) within 5 GeV or 10 GeV of the Z -boson mass. At least one b-jet is required. SR2A and SR2B are optimised for the small mt 1 − mχ0 1 region of the natural GMSB model where low jet multiplicity is expected, whilst SR2C is optimised for the large mt 1 − mχ0 1 region where the jet multiplicity is Table 1 Summary of the event selection in the signal and tt background control regions used in the analysis. The variables used are the number of leptons (N leptons ), the p T of the leading lepton ( p T ( 1 )), the dilepton flavour (SF: same-flavour; DF: different flavour), the dilepton invariant mass (m ), the number of b-jets (N b−jets ), the number of jets regardless of their flavour (N jets ), the p T of the leading jet ( p T (jet 1 )), the p T of the N jets -th jet required in each region ( p T (jet N )), the missing transverse momentum (E miss T ), the transverse momentum of the dilepton system ( p T ( )), and the angular separation in the transverse plane between the leptons forming the SFOS pair ( φ ) Events / 40 GeV high. SR2A is optimised for a stop mass around 400 GeV and SR2B is for 600 GeV. Since the Z boson produced in stop signal events is typically boosted, the transverse momentum of the dilepton system, p T ( ), tends to be high while the azimuthal separation φ tends to be low. This is illustrated by Fig. 1, which shows the p T ( ) distribution after the lepton, m , jet and b-jet requirements in SR2A are applied. Requirements of φ below 1.5 and p T ( ) > 80 GeV or 160 GeV are therefore applied in the SRs. Finally, to enhance the signal contribution, typically with large E miss T due to the LSPs, E miss T > 160 GeV or 200 GeV is required depending on the targeted stop mass.
In the three-lepton SRs (indicated as SR3A and SR3B), at least three signal leptons with two of them forming an SFOS pair with invariant mass which is within 10 GeV of the Z boson mass are required. Two regions are optimised to give good sensitivity in the directt 2 pair production model for differentt 2 −t 1 mass splittings. The SR3A is aimed at signal models with low mass splitting where the Z -boson is not boosted. The SR3B is optimised for high mass splitting where the Z -boson is boosted requiring a minimum p T of the dilepton system of 75 GeV. A high-p T leading lepton with a minimum p T requirement of 40 GeV or 60 GeV for SR3A and SR3B respectively, and at least one b-jet are required to suppress the diboson background. The signal is expected to have higher jet multiplicity than the SM background, due to the presence of two top quarks and two Z bosons. This is illustrated by Fig. 1, which shows the jet multiplicity distribution after the lepton, m , and b-jet requirements in SR3A are applied. Therefore at least five jets are required to increase the signal sensitivity.

Background estimation
Two main sources of background can be distinguished in this analysis: events containing at least one non-prompt or fake lepton (mainly production of multijets and W boson in association with jets in the two-lepton SRs, and production of top pairs and Z boson in association with jets in the threelepton SRs) and events with two or three prompt leptons (mainly Z +jets and tt in the two-lepton SRs, and tt V , t Z, diboson and triboson events in the three-lepton SRs).
Background from fake or non-prompt leptons Fake leptons can originate from a misidentified light flavour quark or gluon jet (referred to as light flavour). Non-prompt leptons can originate from a semileptonic decay of a hadron containing a b-or c-quark (referred to as heavy flavour), or an electron from a photon conversion. The contribution from fake and non-prompt leptons is estimated from data with a matrix method similar to that described in Refs. [84,85]. In order to perform the matrix method, two types of lepton identification criteria are defined: "tight", corresponding to the signal lepton criteria described in Sect. 4, and "loose", corresponding to candidate leptons. To increase the available statistics, muons within a 0.2 < R < 0.4 distance from jets are also considered as loose muons in the method if the scalar sum of p T of charged-particle tracks within a cone of radius R = 0.3 around the muon candidate excluding its own track is less than 30 % of the muon p T . The matrix method relates the number of events containing fake or non-prompt leptons to the number of observed events with tight or loose leptons using the probability for loose prompt, fake or non-prompt leptons to pass the tight criteria. The probability for loose prompt leptons to pass the tight selection criteria is obtained using a Z → data sample and is modelled as a function of the lepton p T . The probability for loose non-prompt leptons to pass the tight selection criteria is determined from data separately for heavy flavour in a bb enriched sample and for photon conversions in a Z → μμγ sample. This probability is modelled as a function of p T and η for electrons and of p T and the number of jets for muons. Simulation studies show that the contribution of fake leptons originating from a misidentified light flavour quark or gluon jet is negligible in all the signal and data control regions used for the background estimation. The probability for loose non-prompt electrons passing the tight selection is calculated according to the fraction of heavy flavour and photon conversion obtained in MC for the different regions.
For SRs with two leptons, relations are obtained for the observed event counts as a function of the number of events containing prompt and non-prompt leptons. These can be solved simultaneously to estimate the number of background events with two tight lepton candidates with at least one nonprompt lepton. In the three-lepton SRs, the background from non-prompt leptons is estimated as in the two-lepton case by considering the leading lepton to be prompt, which simulation studies show to be true in >99 % of the events, and applying the same estimation method to the second and third leading leptons in the event. The results of the estimations have been validated with data in regions with similar background composition obtained by reversing the E miss T or jet multiplicity cuts used in the SRs.

tt background in the two-lepton channel
The dominant background in the two-lepton signal regions comes from tt. The background prediction is normalised to data in dedicated control regions (CRs), and then extrapolated to the SRs. The observed number of events in the CRs are used to derive tt estimates in each of the SRs via a profile likelihood method [86].
The CRs are designed to have kinematic selections as similar as possible to the corresponding SRs in order to minimize systematic uncertainties on the extrapolation of the background to the SR. The CRs use both dilepton events with the same flavour (SF) and different flavour (DF) with the following dilepton mass requirements: 10 GeV < |m − m Z | < 50 GeV (SF), and |m − m Z | < 50 GeV (DF). Except for lepton-flavour dependent systematic uncertainties, SF and DF events are treated in the same way. Apart from the m requirements the CR corresponding to SR2A/B (labelled CR2A) has exactly the same selections as SR2A, whereas the CR for SR2C (labelled CR2C) has a looser E miss T selection than the SR to increase the number of events in the CR.
For the background estimation neglecting any possible signal contribution in the CRs, the fit takes as input the number of expected background events in each CR and SR taken from MC or data-driven estimations and the number of observed events in the CRs. For each SR, the free parameter is the overall normalisation of the tt process. Each uncertainty source is treated as a nuisance parameter in the fit, constrained with a Gaussian function taking into account the correlations between different background sources. The likelihood function is the product of Poisson probability functions describing the observed and expected number of events in the CRs, and the Gaussian constraints on the nuisance parameters. The contribution from all other non-constrained processes are set at the theoretical expectation, but are allowed to vary within their uncertainties. The fitting procedure maximises this likelihood by adjusting the free and nuisance parameters. For the signal models considered in this paper the contamination of the CRs by signal events is small (typically less than 10 %). The expected and observed number of events in the control regions are shown in Table 2. The MC simulation before the fit overestimates the number of tt events observed in both of the CRs. This mis-modelling at high tt transverse momentum ( p T,tt ) has been observed in previous ATLAS analyses [87].

Z +jets background in the two-lepton channel
Background events from Z -boson production associated with jets typically contain fake E miss T due to resolution effects in the jet momentum measurement. Due to the limited statistics and the difficulty of accurately reproducing fake E miss T in MC simulations, a data-driven "jet smearing method" [88] is used to estimate this contribution in the high E miss T tail. In this method, well-measured Z +jets events with low E miss T are selected. By applying jet energy resolution smearing to these events a pseudo-data sample with fake E miss T is gen-erated. The pseudo-data sample is then normalised to data in the E miss T < 80 GeV region, after subtracting other SM background sources estimated by MC for real two lepton events and by the data-driven method for events with nonprompt leptons. Their contribution is less than 10 %. The jet energy resolution smearing function ( p reco T / p truth T ) is initially obtained from multijet MC simulation, where p reco T is the transverse momentum of the reconstructed jet and p truth T is the transverse momentum of the jet constructed from stable truth particles excluding muons and neutrinos. Stable particles are defined as those with a lifetime of 10 ps or more in the laboratory frame. The function is corrected using γ +jet data events where the photon and the jet are balanced. These events are selected by a single photon trigger and require at least one signal photon and one baseline jet. To suppress soft radiation that would affect the p T balance between the jet and the photon, the angle between the leading jet and the leading photon in the transverse plane is required to be larger than 2.9 rad, and the second-leading jet is required to have p T of less than 20 % of the p T of the photon. Using the p T of the balanced photon as reference for that of the jet, the p T response of jets is measured in data and MC. The jet energy resolution smearing function is then modified to match p T response between data and MC. The method is validated by closure tests using MC simulation, and also using data in the 80 GeV < E miss T < 160 GeV region.

Other backgrounds
The estimation of other background processes producing two or three prompt leptons, such as diboson, triboson, tt V , t Z or W t production, is performed using the MC samples described in Sect. 3.
Since tt Z is the main background in the three-lepton SRs and has a topology very similar to at 2 → Zt 1 signal, dedicated validation regions with an enhanced contribution from this background and orthogonal to the SRs are defined to verify the MC prediction in data. These regions are defined requiring at least three leptons and the same m and b-jet requirements as the SRs. In order to enhance the tt Z contribution and reduce the possible contamination from signal events, the events are required to have from three to five jets with p T > 30 GeV and fewer than five jets with p T > 50 GeV. The E miss T is required to be less than 150 GeV except for events with 5 jets with p T > 30 GeV where the E miss T is required to be less than 60 GeV to avoid overlaps with the SRs. The third leading lepton is required to have p T > 20 GeV to reduce the contribution from non-prompt leptons. Two separate validation regions are defined using the p T ( ) variable: VR3A with p T ( ) < 120 GeV and VR3B with p T ( ) > 120 GeV. The contamination from a potential signal can be large in these validation regions but would typically affect VR3A and VR3B differently depend- ing on thet 2 -t 1 mass splitting. Table 3 shows the expected number of events in these validation regions taken from MC or data-driven estimations together with the observed number of events. The expected contribution from selected signal models is also shown. The tt Z contribution is 40-50 % of the total expected event count, and a good agreement with data is observed in both regions.

Systematic uncertainties
The dominant detector-related systematic effects are due to the jet energy scale (JES) and resolution (JER) uncertainties, and the uncertainties on the b-tagging efficiency and mistag rates. The JES uncertainty is derived from a combination of simulation, test-beam data and in-situ measurements [74]. Additional terms accounting for flavour composition, flavour response, pile-up and b-jet scale uncertainties are taken into account. These uncertainties sum to 10-20 % of the total number of estimated background events depending on the SR. JER uncertainties are determined with an in-situ measurement of the jet response asymmetry in dijet events [89], and the impact on the SRs ranges between 1-10 %. Uncertainties associated with the b-tagging efficiency and mistagging of a c-and light-quark jet are obtained from the same techniques used in the derivation of their correction factors. The uncertainty on the expected number of background events in the SR due to b-tagging ranges between 4-10 %.
For the non-prompt lepton background estimation, uncertainties are assigned due to the statistical uncertainty on the number of data events with loose and tight leptons and due to the MC uncertainty on the relative composition of nonprompt electrons (heavy flavour and conversions). The uncertainties on the probabilities for loose leptons to pass the tight selections typically range between 10-45 %, are estimated by using alternative samples for their computation, and include possible dependencies on the lepton p T , η or jet multiplicity. The overall impact of the non-prompt lepton background uncertainties on the expected number of background events are below 2 % in the 2-lepton SRs and approximately 15 % in the 3-lepton SRs.
The uncertainties on the MC modelling of background processes are determined by testing different generators as well as parton shower and hadronisation models. The systematic uncertainties on the modelling of tt+jets, used only to determine the transfer factors between control and signal regions in the two-lepton case, are evaluated by comparing results obtained with the Powheg and Alpgen generators. The hadronisation uncertainty is addressed by comparing Powheg interfaced to Pythia6 with Powheg interfaced to Herwig+Jimmy. The uncertainty related to the amount of ISR/FSR is estimated using the predictions of dedicated AcerMC samples generated with different tuning parameters. The uncertainties on tt are dominated by these theoretical uncertainties after the fit. A 22 % cross section uncertainty is assumed for tt Z and tt W [58]. The uncertainties on the modelling of tt V are evaluated by comparing MadGraph interfaced to Pythia6 with Alpgen interfaced with Her-wig+Jimmy. The uncertainty assigned on the diboson cross sections are 5 % for Z Z [90] and 7 % for W Z [91]. For diboson production processes, the uncertainties on the modelling are evaluated by comparing Powheg interfaced to Pythia8 with the aMC@NLO generator interfaced to Pythia6 and Herwig+Jimmy . For tribosons, tth and t Z production processes, which constitute a very small background in all signal regions, a 100 % uncertainty on the cross section is assumed. The uncertainties on these processes are large to account for kinematic effects, even though the inclusive cross sections are known to better precision.

Results and interpretation
The number of data events observed in each SR for the two-lepton and three-lepton analyses is reported in Table 4 together with the expected SM background contributions. Figs. 2 and 3 show the E miss T distributions for data and background expectations for each SR.
No excess is observed in any of the SRs. The probability ( p 0 -value) of the SM background to fluctuate to the observed number of events or higher in each SR is also reported in Table 4, and has been truncated at 0.5. Upper limits at 95 % CL on the number of beyond the SM (BSM) events for each Table 4 Observed event counts and predicted numbers of events for each SM background process in the SRs used in the analysis. For twolepton SRs, background fit results and nominal MC expectations are given for comparison. The "non-prompt" category includes tt, single top and Z +jets processes for the three-lepton SRs SR3A and SR3B. The p-value of the observed events for the background only hypothesis ( p 0 ) is also shown. The value of p 0 is capped at 0. 5  SR are derived using the CL s prescription [92] and neglecting any possible signal contamination in the control regions. After 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 , defined as the product of acceptance, reconstruction efficiency and production cross section. The limits are calculated from pseudo-experiments as well as with asymptotic formulae [86] for comparison. The results are given in Table 5.
These results are also interpreted in the context of the models described in Sect. 1. Exclusion limits are calculated by combining the results from several exclusive SRs. For the GMSB scenarios, SR2C and SR3A are combined with the region with best expected sensitivity between SR2A or SR2B. For thet 2 simplified models, SR2C is combined with the region with best expected sensitivity between SR3A or obs_x_PR2L1A_met Events / 40 GeV   Table 5 Signal model independent upper limits on the visible signal cross section (σ vis = σ prod × A × ) in the five SRs. The numbers (in parenthesis) give the observed (expected) 95 % CL upper limits. Calculations are performed with pseudo-experiments. The ±1σ variations on the expected limit due to the statistical and background systematic uncertainties are also shown. The equivalent limits on the visible cross section calculated using an asymptotic method are given inside the square brackets expected and observed exclusion limits are calculated using asymptotic formulae for each SUSY model point, taking into account the theoretical and experimental uncertainties on the SM background and the experimental uncertainties on the signal. The impact of the uncertainties on the signal cross section is also addressed for the observed limit only by show- for the directt 2 pair production simplified model with BR(t 2 → Zt 1 ) = 1. The contours of the band around the expected limit are the ±1σ results, including all uncertainties except theoretical uncertainties on the signal cross section. The dotted lines around the observed limit illustrate the change in the observed limit as the nominal signal cross section is scaled up and down by the theoretical uncertainty. All limits are computed at 95 % CL ing the results obtained when moving the nominal cross section up or down by the ±1σ theoretical uncertainty. Quoted numerical limits on the particle masses refer to the signal cross sections reduced by 1σ . Figure 4 shows the limit obtained in thet 2 simplified model, which excludes mt 2 < 525 GeV for mχ0 1 < 240 GeV and mt 2 < 600 GeV for mχ0 1 < 200 GeV. The interpolation of the limit contours between the simulated points towards thet 2 → Zt 1 kinematic boundary has been established using MC generator level information. A reduction in acceptance of up to 20 % is observed in the region where mt 1 decay involves an off-shell Z , has not been considered since in that case othert 2 decay modes, such ast 2 → tχ 0 1 , would be dominant. If the assumption on the 100 % branching ratio for thet 2 → Zt 1 decay mode is relaxed, thet 2 can also decay viat 2 → ht 1 andt 2 → tχ 0 1 . Exclusion limits as a function of thet 2 branching ratios are shown in Fig. 5 for representative values of the masses oft 2 andχ 0 1 . For lowt 2 mass (mt 2 = 350 GeV), SUSY models with BR(t 2 → Zt 1 ) above 10 % are excluded. For higher stop mass (mt 2 = 500 GeV), models with BR(t 2 → Zt 1 ) above 15-30 % are excluded, with a small dependence on the value of the neutralino mass, BR(t 2 → ht 1 ) and BR(t 2 → tχ 0 1 ). In Fig. 6 the expected and observed limits are shown for the GMSB scenarios on thet 1 ,χ 0 1 mass plane. Stop Expected and observed exclusion limits at 95 % CL for the stop natural GMSB model described in the text. The contours of the band around the expected limit are the ±1σ results, including all uncertainties except theoretical uncertainties on the signal cross section. The dotted lines around the observed limit illustrate the change in the observed limit as the nominal signal cross section is scaled up and down by the theoretical uncertainty. For comparison, the observed exclusion limit with 2.05 fb −1 of data at √ s = 7 TeV at ATLAS for a similar model [34] is shown masses up to 540 GeV are excluded for neutralino masses of 100 GeV < mχ0 1 < mt 1 − 10 GeV. In the parameter space region where thet 1 only decays via bχ ± 1 , the exclusion extends up to stop masses of 660 GeV for neutralinos of 550 GeV. For illustration, the exclusion limits obtained with 2.05 fb −1 of ATLAS data at √ s = 7 TeV for the similar model are also shown, in which the maximum limit on the stop masses was 330 GeV. Due to the increase in statistics and the proton-proton collision energy, as well as the optimised selections for these conditions, much stronger constraints are now set on this model.

Summary and Conclusions
This paper presents a dedicated search for direct stop pair production in decays with an experimental signature compatible with the production of a Z boson, b-jets and missing transverse momentum. The analysis is performed with pp collision data at √ s = 8 TeV collected with the ATLAS detector at the LHC corresponding to an integrated luminosity of 20.3 fb −1 . The results are interpreted in the framework of simplified models with production oft 2 as well as in a natural GMSB model. In a simplified model characterised by the decay chaiñ t 2 → Zt 1 witht 1 → tχ 0 1 and the mass difference betweent 1 andχ 0 1 slightly larger than the top mass, parameter space regions with mt 2 < 600 GeV and mχ0 1 < 200 GeV are excluded at 95 % CL. When thet 2 → ht 1 andt 2 → tχ 0 1 decays are included in the model, BR(t 2 → Zt 1 ) > 10-30 % are excluded for several mass configurations. These are the first experimental results on the search fort 2 .
In the GMSB scenario, where thet 1 might decay to bχ ± 1 or tχ 0 1 (χ 0 2 ) and theχ 0 1 decay in ZG or hG, parameter space regions witht 1 masses below 540 GeV are excluded at 95 % CL for 100 GeV < mχ0 1 < mt 1 − 10 GeV. These limits are much stronger than those set on the similar model considered in the search at √ s = 7 TeV. Forχ 0 1 masses of about 550 GeV, better sensitivity is achieved andt 1 masses below 660 GeV are excluded. g Also at CPPM, Aix-Marseille Université and CNRS/IN2P3, Marseille, France