Search for top squark pair production in final states with one isolated lepton, jets, and missing transverse momentum in $\sqrt{s}=$ 8 TeV pp collisions with the ATLAS detector

The results of a search for top squark (stop) pair production in final states with one isolated lepton, jets, and missing transverse momentum are reported. The analysis is performed with proton--proton collision data at $\sqrt{s} = 8$ TeV collected with the ATLAS detector at the LHC in 2012 corresponding to an integrated luminosity of $20$ fb$^{-1}$. The lightest supersymmetric particle (LSP) is taken to be the lightest neutralino which only interacts weakly and is assumed to be stable. The stop decay modes considered are those to a top quark and the LSP as well as to a bottom quark and the lightest chargino, where the chargino decays to the LSP by emitting a $W$ boson. A wide range of scenarios with different mass splittings between the stop, the lightest neutralino and the lightest chargino are considered, including cases where the $W$ bosons or the top quarks are off-shell. Decay modes involving the heavier charginos and neutralinos are addressed using a set of phenomenological models of supersymmetry. No significant excess over the Standard Model prediction is observed. A stop with a mass between $210$ and $640$ GeV decaying directly to a top quark and a massless LSP is excluded at $95$ % confidence level, and in models where the mass of the lightest chargino is twice that of the LSP, stops are excluded at $95$ % confidence level up to a mass of $500$ GeV for an LSP mass in the range of $100$ to $150$ GeV. Stringent exclusion limits are also derived for all other stop decay modes considered, and model-independent upper limits are set on the visible cross-section for processes beyond the Standard Model.


Introduction
The hierarchy problem [1][2][3][4] has gained additional attention with the observation of a new particle consistent with the Standard Model (SM) Higgs boson [5,6] at the LHC [7]. Supersymmetry (SUSY) [8][9][10][11][12][13][14][15][16], which extends the SM by introducing supersymmetric partners for all SM particles, provides an elegant solution to the hierarchy problem. The partner particles have identical quantum numbers except for a half-unit difference in spin. The superpartners of the left-and right-handed top quarks,t L andt R , mix to form the two mass eigenstatest 1 andt 2 , wheret 1 (top squark or stop) is the lighter one. SUSY, if it exists, must be a broken symmetry since the masses of many SUSY particles must exceed those of their SM counterparts. If the supersymmetric partners of the top quarks have masses 1 TeV, loop diagrams involving top quarks, which are the dominant contribution to the divergence of the Higgs boson mass, can be largely cancelled [17][18][19][20][21][22][23][24]. Significant mass splitting betweent 1 andt 2 is possible due to the large top Yukawa coupling 1 . Furthermore, effects of the renormalisation group equations are strong for the third generation squarks, usually driving their masses significantly lower than those of the other generations. These considerations suggest a light stop which, together with the stringent LHC limits excluding other coloured supersymmetric particles up to masses at the TeV level, motivates dedicated stop searches. SUSY models can violate the conservation of baryon number and lepton number, resulting in a proton lifetime shorter than current experimental limits [25]. This is commonly solved by introducing a multiplicative quantum number called R-parity, which is 1 and −1 for all SM and SUSY particles, respectively. A generic R-parity-conserving minimal supersymmetric extension of the SM (MSSM) [17,[26][27][28][29] predicts pair production of SUSY particles and the existence of a stable lightest supersymmetric particle (LSP). In a large variety of SUSY models, the lightest neutralino 2 (χ 0 1 ) is the LSP, which is also the assumption throughout this paper. Since theχ 0 1 interacts only weakly it can serve as a candidate for dark matter.
The stop can decay into a variety of final states, depending amongst other things on the SUSY particle mass spectrum, in particular on the masses of the stop and lightest neutralino. Figure 1 illustrates the simplest decay modes as a function of the stop and LSP masses. In the rightmost wedge, the stop mass is greater than the combined top quark and LSP masses, hence the decayt 1 → tχ 0 1 is kinematically allowed. A lighter stop can undergo a three-body decayt 1 → bWχ 0 1 if the stop mass is still above the combined b + W +χ 0 1 mass. For an even lighter stop, the decay proceeds via a four-body process t 1 → bf f χ 0 1 , where f and f are two distinct fermions, or flavour-changing neutral current (FCNC) processes, such as the loop-suppressedt 1 → cχ 0 1 . If supersymmetric particles other 1 The masses of thet 1 andt 2 are given by the eigenvalues of the stop mass matrix. The stop mass matrix involves the top-quark Yukawa coupling in the off-diagonal elements, which typically induces a large mass splitting. The stop mass matrix is diagonalised by the stop mixing matrix, which gives thet L andt R components of the mass eigenstatest 1 andt 2 .
2 The charginosχ       ( l a r g e -R ) j e t s .
F u r t h 1 6 c o n s t r u c t e d a n d i d e n t i fi e 1 7 n e a r l y m a s s -d e g e n e r a t e˜    Diagrams illustrating the considered signal scenarios, which are referred to as (a) t 1 → tχ 0 1, (b)t 1 → bWχ 0 1 (three-body), (c)t 1 → bf f χ 0 1 (four-body), (d)t 1 → bχ ± 1 . Furthermore, a non-symmetric decay scenario where eacht 1 can decay via eithert 1 → tχ 0 1 ort 1 → bχ ± 1 is considered (not shown). In these diagrams, the charge-conjugate symbols are omitted for simplicity; all scenarios begin with a top squark-antisquark pair.

Analysis strategy
Searching fort 1 pair production in the various decay modes and over a wide range of stop masses requires different analysis approaches. Thet 1 pair production cross-section falls rapidly with increasing stop mass mt 1 : for the range targeted by this search, mt 1 ∼ 100-700 GeV, the cross-section at √ s = 8 TeV proton-proton (pp) collisions decreases from 560 pb to 8 fb. While the varioust 1 decay modes considered all have identical final state objects -one electron or muon accompanied by one neutrino (or more for a leptonic τ decay), two jets originating from bottom quarks (b-jets), two light-flavour jets, and two LSPs -their kinematic properties change significantly for the different decay modes and as a function of the masses of the stop, LSP, and lightest chargino (if present). Dedicated analysis strategies are therefore employed to target the various scenarios. The identification of b-jets (b-tagging) is utilised in the event selections and for constructing kinematic variables. The search for a heavy stop exploits a specialised technique, which reconstructs -4 -several decay products in a single large-radius (large-R) jet. Low-momentum leptons (referred to as soft leptons) are reconstructed and identified to enhance the sensitivity for t 1 → bχ ± 1 decays where theχ 0 1 andχ ± 1 states are close in mass. These and other tools and variables to discriminate signal from background, described in section 6, are used to design sets of requirements for the event selection (each referred to as a signal region, SR), where each set is optimised to target one or more signal scenario. Furthermore, two different analysis techniques are employed, which are referred to as 'cut-and-count' and 'shape-fit'. The former is based on counting events in a single region of phase space (bin), while the latter employs several bins. By utilising different signal-to-background ratios in the various bins, shape-fits enhance the search sensitivity in challenging scenarios, where it is particularly difficult to separate signal from background. All signal regions are described in section 7.
The dominant background in most signal regions arises from dileptonic tt events in which one of the leptons is not identified, or is outside the detector acceptance, or is a hadronically decaying τ lepton. The sub-leading background for most signal regions stems from W +jets production. The tt and W +jets backgrounds are estimated using dedicated control regions (CRs), making the analysis more robust against potential mis-modelling effects in simulated events and reducing the uncertainties on the background estimates. Other small backgrounds are estimated using simulated events normalised to the theoretical cross-sections. Dedicated samples are used to validate the background predictions. The background estimation including the definition of all CRs is detailed in section 8.
The analysis results are based on maximum likelihood fits, which include the CRs to simultaneously normalise the tt and W +jets backgrounds. Systematic uncertainties due to theoretical and experimental effects are considered for all background and signal processes, and are described in section 9. The final results and interpretations, both in terms of model-dependent exclusion limits on the masses of relevant SUSY particles and model-independent upper limits on the number of beyond-SM events, are presented in section 10.

The ATLAS detector
The ATLAS experiment [56] is a multi-purpose particle physics detector with nearly 4π steradian coverage in solid angle. It consists of an inner detector of tracking devices surrounded by a thin superconducting solenoid, electromagnetic and hadronic calorimeters, and a muon spectrometer in a toroidal magnetic field. The inner detector, in combination with the 2 T axial field from the solenoid, provides precision tracking and momentum measurement of charged particles up to |η| = 2.5 and allows efficient b-jet identification. 4 It consists of a silicon pixel detector, a semiconductor microstrip detector and a straw-tube tracker which also provides transition radiation measurements for electron identification. High-4 ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point in the centre of the detector and the z-axis along the beam pipe. Cylindrical coordinates (r, φ) are used in the transverse plane, φ being the azimuthal angle around the beam pipe. The pseudorapidity η is defined in terms of the polar angle θ by η = − ln tan(θ/2), and the angular separation ∆R in the η-φ space is defined as ∆R = (∆η) 2 + (∆φ) 2 .
-5 -granularity liquid-argon (LAr) sampling electromagnetic calorimeters cover the pseudorapidity range |η| < 3.2. The hadronic calorimeter system is based on two different technologies, a scintillator-tile sampling calorimeter (|η| < 1.7) and a LAr sampling calorimeter (1.5 < |η| < 3.2). LAr calorimeters in the most forward region (3.1 < |η| < 4.9) provide electromagnetic and hadronic measurements. The muon spectrometer has separate trigger and high-precision tracking chambers, the former provide trigger coverage up to |η| = 2.4 while the latter provide muon identification and momentum measurements for |η| < 2.7. Events are selected by a three-level trigger system [57], the first level (L1) is implemented in customised hardware while the two high-level triggers (HLT) are software-based.

Trigger and data collection
The data used in this analysis were collected during the period from March to December 2012 with the LHC operating at a pp centre-of-mass energy of √ s = 8 TeV. After application of beam, detector and data-quality requirements, the total integrated luminosity is 20.3 fb −1 with an uncertainty of 2.8%. The uncertainty is derived, following the methodology detailed in ref. [58], from a preliminary calibration of the luminosity scale from beam-separation scans performed in November 2012. The dataset was recorded using three different types of triggers based on requiring an electron, a muon, or large E miss T . The single-electron trigger identifies electrons based on the presence of an energy cluster in the electromagnetic calorimeter with a shower shape consistent with that of an electron, low hadronic leakage, and a matching track in the inner detector. The lower HLT threshold on the energy deposit transverse to the beam (E T ) is 24 GeV. The electron trigger isolation criterion at the HLT requires the scalar sum of the transverse momenta (p T ) of tracks within a cone of radius ∆R = 0.2 around the electron (excluding the electron itself) to be less than 10% of the electron E T . The singlemuon trigger identifies muons using tracks reconstructed in the muon spectrometer and inner detector. The lower p T threshold at the HLT is 24 GeV. An isolation criterion at the HLT requires the scalar sum of the p T of tracks within a cone of radius ∆R = 0.2 around the muon (excluding the muon itself) to be less than 12% of the muon p T . To recover some of the small efficiency loss for high-p T leptons, events were also collected using complementary single-lepton triggers with less stringent shower-shape requirements and without the hadronic leakage criterion for electrons, and with no isolation criteria, but with an increased lower E T (p T ) threshold of 60 GeV (36 GeV) for electrons (muons). Corrections are applied to the simulated samples to account for small differences between data and simulation in the lepton trigger efficiencies.
The E miss T trigger is based on the vector sum of the transverse energies deposited in projective calorimeter trigger towers. A more refined calculation based on the vector sum of all calorimeter cells above noise is made at the HLT. The lower trigger E miss T threshold at the HLT is 80 GeV, and it is fully efficient for offline-calibrated E miss T > 150 GeV in signal-like events. At the beginning of the 2012 data-taking, the E miss T trigger used in this analysis was disabled for the first three bunch crossings of every bunch train, causing a loss of 0.2 fb −1 in integrated luminosity.
-6 -Candidate events in the electron (muon) channel were collected using a logical-OR combination of the single-electron (single-muon) and E miss T triggers. Since the single-lepton trigger thresholds are too high for the soft-lepton selection, these candidate events were recorded using only the E miss T trigger. Consequently, the effective dataset for the soft-lepton selections amounts to an integrated luminosity of 20.1 fb −1 . All results quote a rounded value of 20 fb −1 , while inside the analysis the appropriate integrated luminosity values are used. The efficiency of the E miss T and lepton triggers are measured with W → µν and Z → data samples, respectively. In all cases the combined trigger efficiency is greater than 98% for simulated signal events satisfying the selection criteria for the signal regions described in section 7.

Simulated samples
Samples of Monte Carlo (MC) simulated events are used for the description of the background and to model the SUSY signals. As detailed below, the samples are generated with either POWHEG-r2129 [59], ACERMC-3.8 [60], MadGraph-5.1.4.8 [61], SHERPA-1.4.1 [62] or Herwig++ 2.5.2 [63]. All POWHEG and SHERPA samples use the next-to-leading-order (NLO) parton distribution function (PDF) set CT10 [64], while samples generated with ACERMC, MadGraph or Herwig++ use the CTEQ6L1 [65] PDF set. The ATLAS Underlying Event Tune 2B [66] is used for all MadGraph samples, while the samples generated with POWHEG or ACERMC use the Perugia 2011C [67] tune and samples generated with Herwig++ use UEEE3 [68]. The SHERPA generator has an integrated underlying event tune. The fragmentation and hadronisation for the POWHEG, ACERMC, and MadGraph samples is performed with PYTHIA-6.426 [69], while SHERPA and Herwig++ use their own built-in models.
The samples are processed with a detector simulation [70] using GEANT4 [71] or a fast simulation framework where the showers in the electromagnetic and hadronic calorimeters are simulated using a parameterised description [72] and GEANT4 is used for the rest of the detector. The fast simulation has been validated against full GEANT4 simulation for several signal models and for the main background, tt production. All samples are produced with varying numbers of simulated minimum-bias interactions, generated with PYTHIA-8.160 [73], overlaid on the hard-scattering event to account for multiple pp interactions in the same or nearby bunch crossings (pileup). The average number of interactions per bunch crossing is reweighted to match the distribution in data that varies between approximately 10 and 30.

Background samples
Top quark pair production (tt) is generated with POWHEG for a top quark mass m t = 172.5 GeV. The same top quark mass is used when simulating other signal or background processes involving top quarks. To account for discrepancies between data and simulated tt events at high-p T of the tt system, the simulated sample is reweighted as a function of p T (tt); the weights are based on the ATLAS measurement of the differential tt crosssection at 7 TeV, following the method described in ref. [74]. Single top quark production in the s-channel and the W t mode are also generated with POWHEG, while the t-channel process is generated with ACERMC. In W t production, the interference with tt at NLO in quantum chromodynamic (QCD) is treated by the diagram removal scheme [75]. Associated production of tt and vector bosons (W , Z and W W ) as well as single top production in association with a Z boson, are generated with MadGraph with up to two additional partons. Samples of W +jets and Z/γ * + jets are produced with SHERPA, containing up to four additional partons and the correct treatment of bottom and charm quark masses. The diboson processes (W W , ZZ and W Z) are also generated with SHERPA.
The processes are normalised using theoretical inclusive cross-sections, including higherorder QCD corrections where available. The tt production cross-section is calculated at next-to-next-to-leading order (NNLO) in QCD including resummation of next-to-next-toleading logarithmic (NNLL) soft gluon terms with top++2.0 [76][77][78][79][80][81]. Cross-sections for single top quark production are calculated to approximate NLO+NNLL precision [82][83][84]. The production of tt in association with vector bosons is calculated at NLO [85,86], while the production of a single top quark in association with a Z boson is normalised to the LO cross-sections from the generator, because NLO calculations are only available for t-channel production [87]. The cross-sections for the production of W and Z bosons are calculated with DYNNLO [88]. The production cross-sections for electroweak diboson production are calculated at NLO with MCFM [89,90]. The tt, single top, W , Z, and diboson calculations use the MSTW2008 NNLO PDF set [91], while the cross-sections for tt in association with a vector boson use the MSTW2008 NLO (W ) or CTEQ6.6M [92] (Z) PDF set. The cross-sections for tt and W production are used for the optimisation of the selections, while for the final results the two processes are normalised to data in control regions.

Signal samples
Signal samples of top squark-antisquark pairs are generated with different stop decay and mass configurations. The first scenario assumes thet 1 → tχ 0 1 decay with a branching ratio (BR) of 100%. The samples are generated with Herwig++ in a grid across the plane of t 1 andχ 0 1 masses with a spacing of 50 GeV for most of the plane; the grid is more finely sampled towards the diagonal region where mt 1 approaches m t + mχ0 1 . Thet 1 is chosen to be mostly the partner of the right-handed top quark 5 and theχ 0 1 to be almost pure bino. This choice is consistent with a large BR for the givent 1 decay. Different hypotheses on the left/right mixing in the stop sector and the nature of the neutralino lead to different acceptance values. The acceptance is affected because the polarisation of the top quark changes as a function of the field content of the supersymmetric particles, which impacts the boost of the lepton in the top quark decay. A subset of models where thet 1 is purelỹ t L are studied to quantify this effect and softer distributions of quantities such as lepton p T and m T are observed.
The second signal scenario assumes thet 1 → bχ ± 1 → bW ( * )χ 0 1 decay with a BR of 100%. 6 The stop pairs are always generated with MadGraph, while for thet 1 decay 5 Thet R component is given by the the off-diagonal entry of the stop mixing matrix. Here, this matrix is set with (off-) diagonal entries of approximately (±0.83) 0.55. 6 All possible decays of the (possibly virtual) W boson are considered.
-8 -either MadGraph or PYTHIA is employed. For models where the W boson is on-shell, the fullt 1 decay is performed by MadGraph, while PYTHIA is used to decay thet 1 in models where the W is off-shell. In the latter case, generating the full event with MadGraph would be computationally too expensive. Seven two-dimensional planes are defined to probe the three-dimensional parameter space of thet 1 ,χ ± 1 , andχ 0 1 masses. The typical grid spacing is 50 GeV; higher grid densities are generated in regions where a rapid change of sensitivity is expected. The boundary conditions are derived from the LEP chargino mass limit of 103.5 GeV [30], and by requiring theχ ± 1 mass to be below thet 1 mass. Six out of the seven planes span thet 1 andχ 0 1 masses. The first plane sets the chargino mass to twice the LSP mass (mχ± 1 = 2mχ0 1 ), motivated by the pattern in GUT-scale models with gaugino universality. The second and third planes fix the chargino mass to be above (mχ± 1 = 150 GeV) or close to (mχ± 1 = 106 GeV) the chargino mass limit, respectively. In the fourth and fifth planes the chargino mass and neutralino mass are relatively close, mχ± 1 − mχ0 1 = 5 GeV and mχ± 1 − mχ0 1 = 20 GeV, respectively; small mass differences are motivated by higgsino-like states. The sixth plane sets the chargino mass to be slightly below the stop mass, mχ± 1 = mt 1 − 10 GeV. The last plane fixes the stop mass, mt 1 = 300 GeV, while varying theχ ± 1 andχ 0 1 masses. The samples in all planes assume that thet 1 is at L state. Thet 1 → bχ ± 1 branching ratio might not reach 100% in the MSSM if thet 1 → t +χ 0 1 /χ 0 2 decays are kinematically allowed, but high branching ratios can occur in the allowed parameter space, such as for the above choices of particle field content.
The BR = 100% assumption is relaxed in a third signal scenario where a stop can decay either viat 1 → tχ 0 1 or viat 1 → bχ ± 1 . For this purpose, 'asymmetric' samples are generated where in each event one stop is forced to decay via one and the second stop via the other decay mode. The signal plane as a function of the BR can be probed by combining, with appropriate reweighting, the asymmetric samples with the two BR = 100% samples for thet 1 → tχ 0 1 andt 1 → bχ ± 1 decays. The asymmetric samples are generated with the same generator settings used for the othert 1 → bχ ± 1 samples, except for using the maximum stop mixing angle (yielding equal components oft L andt R ) since the stop mixing is directly related to the BR. The mass points generated are identical to those for the mχ± The three-and four-body stop decay scenarios,t 1 → bWχ 0 1 andt 1 → bf f χ 0 1 respectively, are relevant for a relatively light stop, as shown in figure 1. Samples for each scenario are generated with the assumption of BR = 100%. The three-body samples are produced with Herwig++, which performs the full matrix element calculation of the three-body decay, using the same settings as for thet 1 → tχ 0 1 decay scenario. The four-body decay scenario is generated with MadGraph interfaced with PYTHIA for thet 1 decay and for parton showering, and with up to one additional parton. The four-body decay itself is forced to proceed via a virtual W boson. Thet 1 andχ 0 1 mass parameters are varied with a grid spacing between 25 and 50 GeV.
Signal cross-sections are calculated at NLO, including the resummation of soft gluon emission at next-to-leading-logarithmic accuracy (NLO+NLL) [93][94][95]. The nominal crosssection and the uncertainty are taken from an envelope of cross-section predictions using -9 -different PDF sets and factorisation and renormalisation scales, as described in ref. [96]. Thet 1 pair production cross-section obtained using this prescription is (5.6 ± 0.8) pb for mt 1 = 250 GeV, and (0.025 ± 0.004) pb for mt 1 = 600 GeV. Although the simplified models described above can probe large regions of the allowed SUSY parameter space, more realistic SUSY models can feature more complex stop decays involving the heavier charginos and neutralinos. To study the sensitivity of the various signal regions to these well-motivated scenarios, the pMSSM models described in ref. [97] are used. The models produce a Higgs boson in the mass range (m h = 126 ± 3 GeV), saturate the WMAP relic density [98] and produce values of fine-tuning no worse than 1 part in 100 using the measure proposed by Barbieri, Giudice and Ellis et al. [23,99]. In all models theχ 0 1 is the LSP. To investigate the impact of varying parameters other than the stop and LSP mass while at the same time avoiding the processing of a large number of events, only three differentt 1 andχ 0 1 mass regions are considered. Only models where botht 1 → tχ 0 1 andt 1 → bχ ± 1 are kinematically allowed are used. This serves to remove the models which have a branching ratio of 100% for only one decay scenario, as these regions of parameter space are already probed by the simplified models. This results in a total of 27 models, for which top squark-antisquark pair events are generated with Herwig++ and processed with the fast simulation. Some details of the models are given in table 1. By keeping the stop and LSP masses fixed, the impact on the sensitivity from varying other parameters can be studied, such as the branching ratios to the heavier charginos and neutralinos. The sensitivity for pMSSM models can then be compared to that obtained in the simplified models with the corresponding stop and LSP masses.
6 Physics object reconstruction and discriminating variables

Physics object reconstruction
The reconstructed primary vertex is required to be consistent with the beam diamond envelope and to have at least five associated tracks with p T > 0.4 GeV [100]. If there are multiple primary vertices in an event, the vertex with the largest summed p 2 T of the associated tracks is chosen. Relevant quantities such as the track impact parameters are calculated with respect to the selected primary vertex.
Jets are reconstructed from three-dimensional noise-suppressed calorimeter energy clusters [101] using the anti-k t jet clustering algorithm [102,103] with a radius parameter (R) of 0.4. The impact of pileup is statistically subtracted based on the jet area method [104]. To calibrate the reconstructed energy, jets are corrected for the effects of calorimeter response and inhomogeneities using energy-and η-dependent calibration factors based on simulation and validated with extensive test-beam and collision-data studies. In the simulation, this procedure calibrates the jet energies to those of the corresponding jets constructed from stable simulated particles (particle-level jets). In-situ measurements are used to further correct the data to match the energy scale in simulated events [105,106]. Events containing jets that are likely to have arisen from detector noise, cosmic-ray muons, or machine-induced backgrounds such as beam-gas interactions and beam-halo particles,  are removed [106]. Only jets with p T > 20 GeV are considered. After the overlap removal procedure (described below), jets are required to have |η| < 2.5.
A second collection of anti-k t jets reconstructed with R = 1.0 is used to collect collimated decay products of high-p T top quarks and W bosons; these jets are referred to as large-R jets [107]. The energy calibration is based on the same strategy as used for the jets with R = 0.4 [107]. Jet trimming [108] is applied with a k t sub-jet size R sub = 0.3 and a transverse momentum of the sub-jet relative to the large-R jet, f cut , greater than 0.05. Large-R jets are required to have p T > 150 GeV and |η| < 2.0. The invariant mass of large-R jets is obtained from the energy and momentum of the jet constituents (themselves treated as massless) after the trimming procedure. In addition to the energy calibration, a mass calibration is applied to both data and simulation that accounts for differences -11 -between the jet masses derived at particle-and reconstruction-level. Large-R jets may overlap with other physics objects such as jets or leptons; no overlap removal procedure between large-R jets and other objects is applied. Consequently, large-R jets are neither an input to the calculation of the missing transverse momentum, nor considered for the identification of b-jets.
The identification of b-jets uses the 'MV1' b-tagging algorithm, which exploits both impact parameter and secondary vertex information. The algorithm is based on a neural network that uses the output weights of the IP3D, JetFitter+IP3D, and SV1 algorithms (defined in Refs. [109,110]) and is trained to assign high weights to b-jets and low weights to jets originating from light-flavour quarks or gluons. Three working points are chosen to maximise the search sensitivity for the various selections. They correspond to an average b-tagging efficiency of 60%, 70% and 80% for b-jets with p T > 20 GeV and |η| < 2.5 in simulated tt events. For these three working points, the average rejection factors for light-quark or gluon jets are approximately 600, 140, and 25 in the same simulated tt events [111], respectively. In the simulated samples, the efficiency of identifying b-jets and the probability for mis-identifying (mis-tagging) jets from light-flavour quarks, gluons and charm quarks are corrected to match those found in data.
Electron candidates are reconstructed from energy clusters in the electromagnetic calorimeter matched to a track measured in the inner detector [112,113]. They are required to have p T > 10 GeV, |η| < 2.47, and to satisfy the 'loose' shower shape and track selection criteria [114]. The energy is corrected in data to match simulation, while the reconstruction efficiency is scaled in simulated samples to match that observed in data. Muons are reconstructed and identified either as a combined track in the muon spectrometer and inner detector systems, or as an inner detector track matched with a muon spectrometer segment [115][116][117]. Candidate muons are required to have p T > 10 GeV and |η| < 2.4. Corrections are applied to the momentum and reconstruction efficiency in simulation to match the data. For the soft-lepton selections, the thresholds are lowered to p T > 7 GeV (electrons) and p T > 6 GeV (muons), and electron candidates are required to satisfy the 'medium' identification criteria.
Potential ambiguities between overlapping candidate objects are resolved based on their angular separation. If an electron candidate and a non-b-tagged jet (using the 70% efficiency b-tagging working point) overlap within ∆R < 0.2 of each other, then the object is considered to be an electron and the jet is dropped. If an electron candidate and any jet overlap within 0.2 < ∆R < 0.4 of each other, or if an electron candidate and a b-tagged jet overlap within ∆R < 0.2 of each other, then the electron is dropped and the jet is retained. If a muon candidate and any jet overlap within ∆R < 0.4 of each other, then the muon is not considered and the jet is kept. For the large-R-jet based selection, the last requirement is changed to ∆R < 0.1, still between the muon and the R = 0.4 jets, to recover efficiency losses in boosted topologies. The remaining leptons are referred to as 'baseline' leptons, and are used to veto events with more than one lepton.
Photons are not used in the main selections in this analysis, but they are used to select events for one validation sample. Photon candidates must satisfy the 'tight' quality criteria with p T > 20 GeV and |η| < 2.47 [118,119]. For the validation sample selection only, jets close to a photon, with ∆R < 0.2, are dropped.
An event-veto based on identifying hadronically decaying τ leptons (τ had ) is used in some selections to reject tt background. The τ had candidates are reconstructed in the same way as jets with p T > 15 GeV and |η| < 2.47, but calibrated separately to account for a different calorimeter response. The τ -identification is performed with a boosted decision tree (BDT) discriminator [120,121], which combines tracking information and the transverse and longitudinal shapes of the energy deposits in the calorimeter. If a τ had candidate overlaps with any baseline lepton within ∆R < 0.2, the τ had is not counted.
The missing transverse momentum vector p miss T is the negative vector sum of the p T of reconstructed objects in the event: jets with p T > 20 GeV, charged lepton (electron and muon) and photon candidates with p T > 10 GeV, and calibrated calorimeter clusters not assigned to these physics objects [122,123].
The lepton identification criteria are tightened for the selection of the primary electron or muon in the event. The lepton p T is required to be above 25 GeV, except for the softlepton selections where the baseline thresholds of 7 GeV (electron) or 6 GeV (muon) are kept. Electrons are required to satisfy a variant of the 'tight' selection criteria [114], and are required to satisfy a track-isolation criterion. The scalar sum of the p T of tracks associated with the primary vertex and found within a cone of radius ∆R = 0.2 around the electron (excluding the electron itself) is required to be less than 10% of the electron p T . Similarly, a muon isolation criterion is imposed: the track isolation is required to be less than 1.8 GeV in a cone of radius ∆R = 0.2. A less stringent muon isolation criterion is used for the large-R jet selection: the track isolation is required to be less than 12% of the muon p T . This helps to recover signal efficiency losses in boosted topologies. For the soft-lepton selections, the 'tight' electron selection is omitted (keeping the 'medium' criteria from the baseline selection), and a modified version of the track-isolation is applied to electrons and muons: the scalar sum of the p T of tracks within a cone of radius ∆R = 0.3 around the lepton (excluding the lepton itself) is required to be less than 16% (12%) of the electron (muon) p T . Furthermore, the impact parameters along the beam direction (z 0 ) and in the transverse plane (d 0 ) are used to impose additional soft-lepton requirements: |z 0 sin θ| < 0.4(0.4) mm and |d 0 /σ d 0 | < 5(3) for electrons (muons), where σ d 0 is the uncertainty on d 0 . The modified criteria of the soft-lepton selection are specifically optimised to suppress low-p T jets misidentified as isolated leptons.

Tools to discriminate signal from background
Requiring one isolated lepton ( ), several jets, and E miss T selects a sample enriched in semileptonic tt and W +jets events. Both backgrounds are reduced by requiring the transverse mass (m T ) to be above the W boson mass, where m T is defined by Here p T is the lepton p T , and ∆φ( , p miss T ) is the azimuthal angle between the lepton and the p miss T directions. 7 The dominant background after this requirement stems from dileptonic tt events, where one lepton is not identified, or is outside the detector acceptance, or is a hadronically decaying τ lepton. In all of these cases, the tt decay products include two or more high-p T neutrinos, resulting in large E miss T and large m T values. Requiring one or more b-tagged jets further removes W +jets events, while a b-tag veto reduces the tt background but also the stop signal in most models. All but one signal region require at least one or two b-tagged jets.
A number of variables and tools have been developed specifically to suppress the different types of dileptonic tt events. The detailed definitions of the variables are provided in appendix A.
-am T2 and m τ T2 are two variants of the variable m T2 [124], which is a generalisation of the transverse mass applied to signatures with two particles that are not directly detected. Figure 3 illustrates the tt event topologies targeted by the two variables. The m T2 variable allocates the measured p miss T amongst the number of undetected particles of the assumed topology (neutrinos plus one lost lepton for am T2 , and neutrinos for m τ T2 ); the m T2 calculation is based on particle four-momenta, which requires making assumptions on the masses of the involved particles. For the construction of both m T2 variables, two b-tagged jets are identified based on the highest b-tagging weights.
The first variant is a form of asymmetric m T2 (am T2 ) [125][126][127] in which the undetected particle is the W boson for the branch with the lost lepton and the neutrino is the missing particle for the branch with the observed charged lepton. The parent particles are the top quarks. For dileptonic tt events with a lost lepton, am T2 is bounded from above by the top quark mass, whereas new physics can exceed this bound. The required input masses are m ν for the branch with the visible lepton and m W for the other branch. Both combinations of assigning the two b-tagged jets and the lepton to the two branches are tested, and the final am T2 event value is defined as the minimum of the two. In cases in which the lost lepton is an electron and the corresponding energy deposit enters the E miss T calculation, for instance as a soft calorimeter cluster, am T2 can exceed the top mass boundary in tt events, but the variable remains powerful at discriminating signal from background.
The second m T2 variant (m τ T2 ) is designed for events with a hadronically decaying τ lepton by using the W bosons as parent particles and the 'τ -jet' as a visible particle for one branch and the observed lepton for the other branch. The 'τ -jet' is defined as the highest-p T jet excluding the selected two b-tagged jets. The input masses are set to be zero so that the τ had tt background has an endpoint around the W boson mass in the limit of collinear neutrinos.
topness is a variable designed to identify and suppress partially reconstructed dileptonic tt events, as proposed in ref. [128]. The topness variable is based on minimising a χ 2type function indicating the similarity of the event to dileptonic tt events. Similar to the am T2 variable, one lepton is assumed to be lost; the momentum of the corresponding W boson is a free parameter in the minimisation procedure. If two jets are b-tagged, then each can be assigned to either branch yielding two combinations; if only one b- Figure 3. Illustration of the construction of the am T2 (left) and m τ T2 (right) variables, which are used to discriminate against dileptonic tt background with one lost lepton (left) or with a hadronically decaying τ (right). The dashed lines indicate the objects that are assumed to be undetected ('lost') for the purpose of defining the two variables. tagged jet is present, then the highest-and second-highest-p T jets are considered as the second b-jet resulting in four combinations. All combinations are considered in the minimisation procedure.
-A hadronic top mass, m had−top , is designed to reject dileptonic tt events while retaining signal events that contain a hadronically decaying on-shell top quark, as in thet 1 → tχ 0 1 decay scenario. The m had−top variable is a three-jet invariant mass, where the jets are selected by minimising a χ 2 -distribution taking into account the two jets with the highest b-tagging weights, two additional selected jets, and the p T resolutions of all four jets derived from the jet energy resolution measurements [105,129].
-Dedicated τ -identification criteria are used to reject tt events which contain a hadronic τ decay. For the construction of the τ -veto, the reconstructed τ had candidates, as previously defined, are subject to further selection requirements. Candidates are required to have either one associated track (classified as one-prong τ decay), or two to three tracks (classified as three-prong τ decay, where one track can be missed). The τ had charge for candidates with one or three tracks is required to be ±1 and to be opposite to the charge of the selected electron or muon in the event. For candidates with two tracks, an opposite charge-sign requirement is applied only if the τ had charge is ±2. Finally, three different BDT requirements are imposed on the candidates to define three τ -veto working points: loose, tight, and extra-tight. In simulated tt events with one W → ν decay, signal-and background-like events are defined by requiring the other W boson to either decay into quarks (signal) or into a τ had (background). In these samples, the loose (tight) τ -veto retains 99% (97%) of signal events, while for background events 81% (69%) with a one-prong and 75% (63%) with a three-prong τ had decay survive the veto.
-A track-veto is designed to reject events which contain an isolated track not associated -15 -with a baseline lepton. This complements the second-lepton veto, and helps to reject tt events with a one-prong τ had . Tracks are required to satisfy the following criteria: p T > 10 GeV and |η| < 2.5, transverse and longitudinal impact parameters |d 0 | < 1 mm and |z 0 | < 2 mm. The track isolation requires that there are no additional tracks associated with the primary vertex with p T > 3 GeV in a cone of ∆R = 0.4 around the track. Events with at least one isolated track of opposite charge compared to that of the selected electron or muon in the event are rejected by the track-veto.
Multijet events can pass the event selection if a jet is mis-identified as a lepton or when a real lepton from a heavy-flavour decay satisfies the isolation criteria, and if large E miss T occurs due to mis-measured jets. The former is suppressed by the lepton isolation criteria, while the following variables are used to reduce the latter effect.
-∆φ(jet i , p miss T ), the azimuthal opening angle between jet i and p miss T , is used to suppress multijet events where p miss T is aligned with a jet.
where H T is defined as the scalar p T sum of the four leading jets, is an approximation of the E miss T significance.
-H miss T,sig is an object-based missing transverse momentum, divided by the per-event resolution of the jets. It is defined by where H miss T is the negative sum of the jets and lepton vectors. The denominator is computed from the per-event jet energy uncertainties, while the lepton is assumed to be well-measured. The parameter M is chosen to be a characteristic 'scale' of the background [130], and is fixed at 100 GeV in this analysis based on optimisation studies.

Signal selections
Signal selections are optimised using simulated samples only. The metric of the optimisation is to maximise the exclusion sensitivity for the various decay modes, and for different regions of SUSY simplified model parameter space. A set of signal benchmark models, selected to cover the various stop scenarios, was used for the optimisation considering all studied discriminating variables and including statistical and systematic uncertainties. The shape-fits employ multiple bins in one or two discriminating variables, which were selected considering the signal and background separation potential, inter-variable correlations, systematic uncertainties, and modelling of the data. 600 GeV, with a large-R jet cut-and-count 4 cut-and-count 7  labels begin with tN, which is an acronym for 'top neutralino'; additional text in the label describes the stop mass region, for example tN diag targets the 'diagonal' of thet 1 -χ 0 1 mass plane. Nine SRs target thet 1 → bχ ± 1 decay, where the SR labels follow the same logic: the first two characters bC stand for 'bottom chargino', a third letter ('a' to 'd') denotes the four different mass hierarchies illustrated in figure 4, and the last piece of text describes the stop mass region. Furthermore, two SRs labelled 3body and tNbC mix are dedicated to the three-body decay scenario (t 1 → bWχ 0 1 ), and the mixed scenario wheret 1 → tχ 0 1 and t 1 → bχ ± 1 decays both occur, respectively. The SRs are not mutually exclusive. All SRs employ selection requirements to suppress the multijet background, and most SRs use the tools described in section 6.2 to reduce the dileptonic tt background. Shape-fit techniques are employed to derive model-dependent exclusion limits where useful, while 1 Introductioñ Signal! Regions for all model-independent results a simple cut-and-count approach is used. This procedure implies that for SRs using shape-fits, one bin is probed at a time to extract the modelindependent results. Only a single bin, or the four bins with highest signal-to-background ratio are included; these are referred to as signal-sensitive bins. The tables describing the SR selections specify the techniques and regions used for the model-independent and model-dependent results, referred to as 'discovery setup' and 'exclusion setup'.

Event preselection
Common preselection criteria are employed as follows. Events are required to contain a reconstructed primary vertex. Furthermore, a set of quality requirements to avoid badly reconstructed jets, mismeasured-E miss T and detector-related problems is imposed on all events. Events with a bad quality muon or with a cosmic-ray muon candidate 8 are rejected.
Exactly one isolated lepton is required with p T > 25 GeV except for the soft-lepton selections which employ a p T > 6(7) GeV requirement for muons (electrons). The common lepton isolation criteria are tightened for the soft-lepton selections while they are relaxed for the large-R jet selection (cf. section 6). Events containing additional baseline leptons are rejected. A minimum number of jets ranging between 2 and 4, and E miss T > 100 GeV are common requirements amongst all signal regions. Table 3 summarises the preselection criteria. Figure 5 illustrates the separation power for a selection of discriminating variables. For these distributions, events are required to pass the preselection (table 3), to have at least four jets with p T > 25 GeV, one of which above 60 GeV, and with at least one of them b-tagged using the 70% working point, and to have m T > 60 GeV and E miss T / √ H T > 5 GeV 1/2 . The W +jets background is normalised to match data in a sample selected in the same way, except that a b-veto is imposed. The other processes are normalised to Data quality jet and E miss T cleaning, cosmic-ray muon veto, primary vertex.
Lepton one isolated electron or muon with p T > 25 GeV; soft lepton: the p T threshold is 6(7) GeV for muons (electrons).

Jets
The minimum jet multiplicity requirement varies between 2 and 4.  their theoretical cross-sections. Data and background estimation are seen to be in good agreement.
7.2 Selections for thet 1 → tχ 0 1 decay Stop pair production with subsequentt 1 → tχ 0 1 decays leads to final state objects similar to that of tt production augmented by twoχ  Table 4 details the event selections for these signal regions. Criteria based on a subset of the variables outlined in section 6.2, as well as optimised jet thresholds, a more stringent E miss T requirement, and a requirement on the angular separation between the highest-p T b-tagged jet and the lepton, ∆R(b -jet, ), are used to suppress tt and W +jets backgrounds as well as to reduce the multijet background to a negligible level.
The loosest selection, tN diag, employs a multi-binned shape-fit that targets the challenging parameter space where the stop and its decay products are nearly mass degenerate (mt 1 m t + mχ0 1 ), also referred to as the 'diagonal'. The strategy of exploiting binned shape information significantly improves the sensitivity. The two-dimensional shape-fit in the variables m T and E miss T is illustrated in figure 6 (left plot). The top 12 bins serve both to probe a signal and to normalise the tt background; a subset of the 12 bins has a high purity in tt events. Three additional bins with a b-tag veto, shown in the bottom part, are used to derive the normalisation of the W +jets background. The bins with E miss T > 150 GeV or m T > 140 GeV are defined without upper boundaries.
The two signal regions tN med and tN high target medium and high stop mass regions, respectively. The tN med SR is designed for a stop mass of ∼ 550 GeV and with LSP masses up to ∼ 225 GeV, while the tN high SR is optimised for a stop mass of ∼ 700 GeV and a massless LSP. Both SRs are based on a cut-and-count approach with relatively tight selections. The dominant background arises from dileptonic tt events followed by W +jets production. The tt + Z(→ νν) background has a cross-section about three orders of magnitude smaller than tt production, but is an irreducible background for stop signals. As a consequence, the tt + Z(→ νν) process becomes a relevant background for tight selections such as tN high, where its expected yield is at the same level as for W +jets.
The SR labelled tN boost also targets a stop mass of ∼ 700 GeV and a nearly massless LSP, but takes advantage of the 'boosted' topology of such a heavy stop decay. The Exclusion setup shape-fit in m T and cut-and-count E miss T , cf. figure 6.
Discovery setup test signal-sensitive cut-and-count bins one-by-one. Table 4. Selection criteria for SRs employed to search fort 1 → tχ 0 1 decays. The details of the exclusion and discovery setups can be found in section 10. selection assumes that either all decay products of the hadronically decaying top quark, or at least the decay products of the hadronically decaying W boson, collimate into a jet with a radius of 1.0. Figure 7 shows some of the relevant large-R jet related distributions. The overlaid heavy stop benchmark model illustrates the separation power of the variables. The cut-and-count event selection of tN boost requires at least one large--21 -   Figure 6. Schematic illustration of the tN diag (left) and 3body (right) shape-fit binning. The m T and E miss T (left) or am T2 (right) variables are used to define a matrix of 4 × 3 bins (left) or 3 × 4 (right) in the top part, which is sensitive to stop models, while also being enriched with tt background. The bottom bins invert the b-tag requirement into a veto, and serve to normalise the W +jets background. The numbers of observed events together with the estimated background, obtained using the background-only fit described in section 8, are given for each bin. The data and estimated background are in perfect agreement in the six bottom bins for the left plot because the fit is configured to use these six bins together with six free parameters; the fit used for the right plot employs the bottom eight bins and two free parameters. For comparison the expected numbers of events for one signal model are shown.
R jet with p T > 270 GeV and an invariant mass above 75 GeV. To further discriminate stop decays from the tt background, events with a second (ordered by p T ) large-R jet are required to have a minimum azimuthal distance between p miss T and the second large-R jet, ∆φ(jet large-R 2 , p miss T ) > 0.85. The extra-tight τ -veto is modified to only discard events with τ had candidates well separated from large-R jets, ∆R(τ had , large-R-jet) > 2.6, that satisfy the above p T and mass requirements. Additional signal and background separation is achieved using the m T , E miss T , am T2 and topness variables, leading to dileptonic tt, W +jets, and tt + Z(→ νν) production as the dominant backgrounds.

Selections for thet
Nine SRs target scenarios where both stops decay ast 1 → bχ ± 1 followed by subsequent χ ± 1 → W ( * )χ 0 1 decays. The mass of the lightest chargino m(χ ± 1 ) relative to thet 1 andχ 0 1 masses largely defines the kinematic properties. Figure 4 schematically illustrates the four distinct mass hierarchies, whose signal regions are described below.

Selections for mass hierarchy (a):
The selection of signal events with a small overall mass splitting, ∆M = m(t 1 ) − m(χ Events are required to pass the preselection defined in section 7.1. In addition, the jet thresholds are tightened (p T > 75, 65, 40, 25 GeV) and a requirement of m T > 120 GeV is imposed. The uncertainty band includes statistical and all experimental systematic uncertainties. The last bin includes overflows. A benchmark signal model, with cross-section enhanced by a factor of 100, is overlaid for comparison. a soft lepton and relatively soft sub-leading jets. The leading jet must not satisfy the b-tagging criteria, while at least one b-tagged jet amongst the sub-leading jets is required; Two SRs, labelled bCa low and bCa med, are defined to probe scenarios with a mass splitting ∆M 50 GeV, and 50 GeV ∆M 80 GeV, respectively. The SR event selections are listed in table 5. The requirement of ≥ 3 jets suppresses the W +jets background in bCa med. For bCa low, the jet multiplicity requirement is lowered to ≥ 2 to avoid large bCa low bCa med bCb med1 bCb high Preselection soft-lepton preselection, cf. table 3.   signal acceptance losses, but tighter E miss T and E miss T /m eff thresholds are applied to keep the W +jets and multijet backgrounds suppressed. Figure 8 compares data with estimated backgrounds in the lepton p T and E miss T /m eff distributions. Events in these distributions are required to satisfy the soft-lepton preselection criteria (cf. table 3), have m T > 40 GeV, and contain two or more jets (p T > 130, 25 GeV) of which the leading one must not be b-tagged while the sub-leading one is required to be b-tagged. The overlaid stop benchmark model motivates the selection of low-p T leptons, and the background estimates show the non-negligible contribution from multijet events (with mis-identified leptons). The tt and W +jets backgrounds are normalised using control regions, the multijet background is estimated directly from data, and all other backgrounds are normalised to their theoretical predictions (as described in section 8).
Exclusion results are obtained using a shape-fit in the lepton p T variable with four bins of approximately uniform widths in the range [6(7), 50] GeV for muons (electrons). For model-independent results, the cut-and-count approach is used with an additional lepton p T < 25 GeV requirement.

Selections for mass hierarchy (b):
Signal scenarios with a moderately large ∆M but a small ∆m = m(χ ± 1 ) − m(χ 0 1 ) feature two high-p T b-jets and low-momentum decay products from the two off-shell W bosons.
Two SRs, labelled bCb med1 and bCb high, employ event selections based on the presence of one soft lepton and two b-tagged jets. They target medium (200 GeV m(t 1 ) 500 GeV) and high (500 GeV m(t 1 ) 600 GeV) stop mass regions, respectively. The complete event selections are listed in table 5. The bCb med1 SR employs an E miss T > 150 GeV requirement, the lowest possible to retain full E miss T trigger efficiency. For models with a heaviert 1 , a higher E miss T threshold improves the sensitivity. The dominant background stems from tt production and is suppressed by vetoing additional hard jet activity. The variable H T,2 is defined like H T but without including the two leading jets. The bCb high SR omits the jet activity veto to compensate for the loss in signal acceptance associated with the more stringent E miss T requirement. Beyond the kinematic am T2 bound, the dominant source of background arises from mis-tagged c-jets in semileptonic tt events, and the production of a W boson in association with heavy-flavour jets. To minimise the mis-tagged background, the b-tagging algorithm is operated at the 60% efficiency working point. The invariant mass of the two b-tagged jets, m bb , is required to be above 150 GeV to reduce the contribution from W + bb events.
Exclusion results are obtained using a shape-fit in the am T2 variable with six bins in the range [0, 500] GeV with a uniform bin width. For all model-independent results, the cut-and-count approach is used but applying an am T2 > 170(200) GeV requirement in bCb med1 (bCb high).   Figure 9. Schematic illustration of the bCb med2 (left) and bCd bulk (right) shape-fit binning. More details are given in the caption of figure 6. The data and estimated background are in perfect agreement in the six bottom bins of the right plot because the fit is configured to use these six bins together with six free parameters; the fit used for the left plot employs the bottom four bins and two free parameters.
A third SR, labelled bCb med2, also targets intermediate stop masses. It is based on the default lepton selection (p T > 25 GeV), and requiring at least two high-p T b-tagged jets to exploit largert 1 -χ ± 1 mass splittings than bCb med1. The full event selection is detailed in the leftmost column in table 6. The analysis employs a two-dimensional shape-fit technique similar to the one used for tN diag but in the m T and am T2 variables. Figure 9 (left plot) illustrates the configuration. The highest signal sensitivity is obtained from bins in the top-right region.

Selections for mass hierarchy (c):
Models with mχ± 1 just below mt 1 yield two low-momentum b-jets. The signal selection strategy is based on vetoing events with b-tagged jets, assuming both signal b-jets are below the jet p T acceptance of the analysis, and therefore suppressing the tt background. The sensitivity for low-m(t 1 ) models is improved by selecting events with ISR-like jet activity. A single cut-and-count SR, labelled bCc diag, is employed and defined in table 6. The suffix 'diag' refers to the diagonal region of the mχ± 1 = 2mχ0 1 scenario, the benchmark region used to optimise this SR. The event selection includes one central lepton (|η| < 1.2) to suppress the W +jets background, and three or more jets, of which none must satisfy the b-tagging criteria. In signal events, two of the three required jets tend to originate from the hadronic W boson decay, while the highest-p T jet typically arises from ISR. The b-veto strongly suppresses tt events, leaving W +jets as the dominant background. Requirements on the ∆R(j 1 , ) and E miss T variables further enhance the signal-to-background ratio, by selecting events where the two stops recoil from an ISR jet. Exclusion setup shape-fit in m T and am T2 , cut-and-count shape-fit in m T and am T2 , cut-and-count cf. figure 9. cf. figure 9.
Discovery setup test signal-sensitive bins. cut-and-count test signal-sensitive bins. cut-and-count Table 6. Selection criteria for SRs employed to search fort 1 → bχ ± 1 decays. The first SR targets mass hierarchy (b), the next SR is designed for mass hierarchy (c), and the last three SRs are optimised for mass hierarchy (d), as illustrated in figure 4.

Selections for mass hierarchy (d):
Signal models with relatively large mass splittings between the three mass states,t 1 , χ ± 1 , andχ 0 1 , result in events where all particles from the twot 1 decays are well above the identification p T thresholds. The event selection is based on one lepton and four or more jets, including at least one b-tagged jet.
Three SRs, labelled bCd bulk, bCd high1, and bCd high2, target specific mass regions. The first SR is optimised fort 1 masses up to ∼ 500 GeV and requires ≥ 1 b-tagged jet. The latter two SRs are designed fort 1 masses above ∼ 500 GeV; both require ≥ 2 b-tagged jets, and the main differences between the two regions are the p T thresholds of the two b-tagged jets. The more stringent requirements in bCd high2 with respect to those in bCd high1 are designed to target models with larger stop-chargino mass splittings. Table 6 details the event selections.
The bCd bulk SR employs a two-dimensional shape-fit technique with bins in the m T − am T2 plane. Figure 9 (right plot) illustrates the binning. Compared to bCb med2, which uses the same two variables in a shape-fit, a loose and more inclusive event selection is employed. The bCd high1 and bCd high2 SRs are based on rather tight event selections, leading to relatively low expected background yields. The dominant backgrounds for all three SRs are tt and W +jets production.

Selections for the mixed, three-and four-body decays
Three additional stop decay scenarios are considered: Events wheret 1 → tχ decays are both allowed, with the branching ratios of the two decays summing to one; both stops decay via a three-body process (t 1 → bWχ 0 1 ); and both stops undergo a four-body decay (t 1 → bf f χ 0 1 ). In the mixed decay scenario, the two cases of a very large and a very low BR(t 1 → tχ 0 1 ) are well covered by the signal selections targeting the puret 1 → tχ 0 1 andt 1 → bχ ± 1 decays, respectively. A dedicated cut-and-count SR with the label tNbC mix is optimised for the mixed case with BR(t 1 → tχ 0 1 ) ∼ 0.5. It is based on selecting events with one lepton and four or more jets of which at least one is b-tagged. In addition to the common requirements, the tNbC mix SR employs a requirement on the topness variable, which was designed specifically for the mixed decay scenario, to suppress the dominant dileptonic tt background. The diboson background is suppressed by placing a loose upper requirement on the three-jet invariant mass, m jjj . Diboson events that pass the selection tend to have a leptonic W boson decay and a hadronic W or Z decay, accompanied by at least two additional jets. Large E miss T can be generated by the neutrino when the diboson system is sufficiently boosted; the two additional jets hence typically arise from ISR activity. The three-jet mass requirement effectively reduces this type of background. The jet-jet pair with an invariant mass above 60 GeV that has the smallest ∆R is selected to form the hadronic V boson. The mass m jjj is reconstructed from the third jet closest in ∆R to the hadronic V boson momentum vector. Table 7 lists the entire event selection.
A dedicated signal region labelled 3body is optimised for the three-body decay scenario. Compared to the scenario with on-shell top quarks, three-body decays yield the same final state objects but with significantly lower momenta, although typically still above the tNbC mix 3body
Exclusion setup cut-and-count shape-fit in m T and am T2 , cf. figure 6.
Discovery setup cut-and-count test signal-sensitive bins one-by-one. reconstruction thresholds. The event selection is based on one lepton with p T > 25 GeV and four or more jets, of which at least one is required to be b-tagged. While the semileptonic tt and W +jets backgrounds are suppressed for m T > m W , the dileptonic tt background is separated from signal in the very low am T2 regime. The three-body signal peaks in am T2 below around 100 GeV due to the kinematic construction of the variable and the fact that m(t 1 ) − m(χ 0 1 ) is below the top quark mass. A two-dimensional shape-fit technique using the m T and am T2 variables is employed, similar to that used in bCd bulk and bCb med2, but with different binning. The configuration is illustrated in figure 6(right plot). Fine binning is used in the low am T2 region where the highest signal sensitivity is obtained. The full 3body event selection (detailed in table 7) is applied to all events distributed amongst 16 mutually exclusive bins, but the b-tag requirement is inverted for the W +jets control region bins.
The four-body decay scenario is characterised by events with final state objects that -29 -tend to have even lower momenta than for three-body decays. The selections based on a soft lepton designed for the overall 'compressed' mass hierarchy (a) provide good search sensitivity for this scenario.

Background estimates
The dominant sources of background are the production of tt events and W +jets where the W decays leptonically. Other background processes considered are single top, dibosons, Z+jets, tt produced with a vector boson (ttV ), and multijet events.
The tt and W +jets backgrounds are estimated by isolating each of them in a dedicated control region, normalising simulation to match data in that control region, and then using simulation to extrapolate the background predictions into the signal region. A detailed description of the method and its validation are given below.
The multijet background is estimated from data using a matrix method described in refs. [131,132]. The contribution is found to be negligible for all but the soft-lepton selections. All other (small) backgrounds are determined entirely from simulation, normalised to the most accurate theoretical cross-sections available (cf. section 5).

Control regions
Each cut-and-count SR has two associated CRs which are enriched in either tt events (TCR) or W +jets events (WCR). The two orthogonal CRs are used to normalise the corresponding backgrounds in data, specifically for the associated SR. For the shape-fits, bins enriched in tt or W +jets events are either already part of the full set of bins and act as CRs or are included as additional CR bin(s). The CRs are designed to select events as similar as possible to those selected by the corresponding SR while keeping the contamination from other backgrounds and potential signal low. The CRs are also chosen to retain a sufficiently large number of events to not be limited by the statistical precision. This background estimation approach improves the robustness against potential mis-modelling effects in simulation since the dependence on simulation is reduced, and hence it reduces the uncertainties on the background estimates.
A likelihood fit is performed for each SR, involving all associated bins: SR, TCR, WCR for cut-and-count or all bins of a shape-fit. Each bin is modelled by a separate probability density function based on a Poisson term, where the expected number of events is given by the sum over all background processes, and optionally a signal model. The normalisation of the tt and W +jets backgrounds is controlled by two (or more for some shape-fits) free parameters in the fit. The background parameters are shared across all (several, in case of some shape-fits) bins, and are predominantly constrained by CRs which have many events. To obtain a set of background predictions that is independent of the observation in the SRs, the fit can be configured to use only the CRs to constrain the fit parameters: the SR bins (or signal-sensitive bins in shape-fits) are removed from the likelihood and any potential signal contribution is neglected everywhere. This fit configuration, referred to as the background-only fit, is used throughout this section. The treatment of systematic uncertainties in the likelihood fits is discussed in section 9. To quantify a potential excess, -30 - or to derive exclusion limits, the SR bins are included in the likelihood, as further detailed in section 10.
The key observable used to define the TCR and WCR for most SRs is the transverse mass. Figure 10 shows the m T distribution for events passing the preselection defined in section 7.1 and with ≥ 1 (left) or ≥ 2 b-tagged jets (right) using the 70% and 80% working points, respectively. The tt and W +jets backgrounds drop sharply beyond the W boson mass, while signal events can exceed this kinematic endpoint due to the two additional LSPs in the event. Most TCR and WCR definitions differ from the associated SR by the m T requirement, which is set to 60 GeV< m T < 90 GeV for the CRs. For the four SRs based on a soft lepton, which employ one-dimensional shape-fits for setting model-dependent exclusion limits, the two CRs are defined by loosening the E miss T and m T requirements (bCa med and bCa low), or the soft-lepton selection of 6(7) GeV < p T ( ) < 25 GeV for muons (electrons) in the SR is changed to a p T ( ) > 25 GeV requirement in the CRs (bCb med1 and bCb high). The same two CRs are used for the discovery and the exclusion setup for all cut-and-count selections and for the four one-dimensional shape-fits. The CRs of the four two-dimensional shape-fits are described below. All WCRs have a b-tag veto instead of a b-tag requirement to reduce the tt contamination; consequently all requirements related to the presence of a b-jet are removed. The b-tag requirement used in all but one SR enhances the heavy-flavour contribution of the W +jets background, while the WCRs with the b-tag veto predominantly select light-flavour W +jets events. A systematic uncertainty and a dedicated validation related to this effect are described in section 9 and in the next subsection, respectively. The TCRs employ the same b-tagging requirement as used in the associated SRs, except for bCc diag where the b-tag veto in the SR is turned into a ≥ 1 b-tag requirement in the TCR (using the same b-tagging working point as for the b-tag veto in the SR). Furthermore, some other kinematic requirements are slightly loosened or removed to increase the event yields in the CRs. The event selections for all CRs associated with cut-and-count or one-dimensional shape-fit selections are specified in table 8.
The four two-dimensional shape-fits (tN diag, 3body, bCb med2, and bCd bulk) have built-in bins enhanced in tt events, which act as TCRs, while additional WCR bins are added with a b-tag veto and with a 60 GeV< m T < 90 GeV requirement (as can be seen in figures 6 and 9). For the background-only fits, the WCRs and the subset of the TCR shape-fit bins with m T < 90 GeV are used to constrain the likelihood fit. The tt and W +jets backgrounds are normalised separately in each E miss T or am T2 slice in the tN diag and bCd bulk shape-fits, as these two have sufficiently large numbers of events in the lowm T bins. Thus, there are three tt and three W +jets normalisation parameters, which are applied to all m T bins in the given E miss T or am T2 range. This approach increases the robustness of the fit against potential mis-modelling in the simulation at the expense of a reduced statistical precision. For the other two shape-fits with lower event yields, 3body and bCb med2, one tt and one W +jets normalisation parameter is applied across all bins. All shape-fit bins are used to extract model-dependent exclusion limits, while a subset is used for the model-independent results and for the background only fits. This subset includes all bins with m T < 90 GeV, acting as CR bins, and in addition for the model-independent results one signal-sensitive bin is included.
Top pair and W +jets production accounts for 70-80% of events in the TCRs and WCRs. The signal contamination, for all signal models studied and all CRs, is typically at the percent level and never exceeds 10%. It is explicitly taken into account when setting model-dependent exclusion limits. Table 9 shows the background predictions in each signal region. The number of tt and W +jets events are estimated using the background-only fit. For the four two-dimensional shape-fits, the background predictions are given for the four bins with the highest signalsensitivity. The quoted uncertainties include all statistical and systematic effects, described in section 9. The numbers of tt events normalised in the various TCRs are compatible with the predictions entirely based on simulation and the theoretical cross-section, while the W +jets estimates are about 30% lower than, but nonetheless compatible with the predictions from simulation normalised to the theoretical cross-section. Tables showing the estimated and fitted number of background events in the control, validation and signal regions of the cut-and-count analyses and all bins of the shape-fits are shown in appendix B.

Validation
The background fit predictions are validated using dedicated event samples, referred to as validation regions (VRs). One or more VRs are defined for each of the tt and W +jets backgrounds. The VRs are designed to be kinematically close to the associated SRs to test the background estimates in regions of phase space as similar as possible to the SRs. For most SRs the associated VRs are defined following a similar strategy as used for the CRs but with a 90 GeV < m T < 120 GeV requirement, which leads to a set of events orthogonal -32 - All bCa * p T ( ) > 6(7) > 6(7) [6(7),25] [6(7),25] [6(7),25/50]   Table 8. Event selections for control regions, validation regions, and the discovery-setup signal regions (defined in tables 4-6) associated with cut-and-count or one-dimensional shape-fits. The asterisk symbol '*' is used as a wildcard to describe variable requirements common to several regions. Only one validation region is defined for the bCb med1 and bCb high selections. Variables for which the requirements are the same between the regions are not listed. Requirements related to the presence of a b-tagged jet are removed in all selections with a b-tag veto (WCRs and WVRs  Table 9. Background estimates in each signal region (discovery setup) obtained from control regions for tt and W +jets, from data for multijet events, and from simulation normalised to theoretical cross-sections for all other backgrounds. The quoted uncertainties include all statistical and systematic effects. The sum in quadrature of the uncertainties of all backgrounds may not add up to the total uncertainty due to correlations.
-34 -to both the associated CRs and the SR. The event selections for the tt and W +jets VRs, TVR and WVR respectively, are given in table 8. Another set of tt validation regions, referred to as TVR2 but not shown in the table, is defined where applicable by inverting the SR requirement on am T2 while keeping all other requirements the same as in the SR. For the four two-dimensional shape-fits, a subset of the shape-fit bins in the region falling in between that dominated by tt and the region enhanced by a potential signal is used for the tt background validation.
For the cut-and-count selections, the VRs are not used in the fit to constrain the fit parameters. Instead, the number of background events in each VR is predicted by the fit (using simulation for the extrapolation) and compared to the data, as shown in the upper panel of figure 11. The lower panel shows the pull for each VR, where the pull is defined as the difference between the predicted background and the observed number of events divided by the total uncertainty. The latter is given by the full uncertainty of the prediction (described in section 9) added in quadrature with the statistical uncertainty of the observed number of events. The results are obtained using the background-only fit configuration. No indication of background mis-modelling is found. VRs belonging to different signal regions can share events, and the systematic uncertainties are correlated across different regions and bins.
In addition to the VRs, several other cross checks are performed to further validate the background estimations. For the SRs requiring more than two jets, dileptonic tt events can pass the event selection only if they contain additional jets beyond the two b-jets from the leading-order description of the decay. The modelling of these additional jets, which in the simulation arise from radiation or higher-order-corrections, and which is relevant for the background estimation, is validated using a dedicated sample. The event selection is based on requiring one isolated electron and one oppositely-charged, isolated muon, as well as two or more jets of which at least one is b-tagged using the 70% working point. This selects a clean sample of tt events, which is used in figure 12 (left) to compare the jet multiplicity distributions between data and simulation. Data is modelled sufficiently well within the systematic uncertainties. Further dedicated validation samples are used to test the modelling of the tt background with a τ had or isolated track. These samples are based on the common event preselection and inverting either the track-or τ -veto. The simulation is found to model data well within uncertainties.
The W +jets light-vs heavy-flavour composition in the WCR can be different from that in the SR. A dedicated validation is performed by selecting a sample enriched with W +heavy-flavour jets events. The event selection is based on exactly one isolated lepton, and exactly three jets (the fourth jet veto reduces tt events), of which at least one is btagged. Furthermore, events are required to have 60 GeV< m T < 90 GeV, E miss T > 150 GeV, and the two jets with the highest b-tagging weights are required to yield an invariant mass below 80 GeV and to have a limited separation in η-φ space to increase the sensitivity to pair-produced heavy-flavour jets in association with a W boson. The selected sample of 166 events has a predicted W +heavy-flavour jets component of about 40%; data are found to be in good agreement with simulation, predicting 171 events, when the overall W +jets -35 - [90,120] T [100,125] Figure 11. The upper panel compares data with background predictions in each validation region and a set of signal-depleted shape-fit bins. The lower panel shows the pull of the same bins. The tt and W +jets background estimates are obtained using the background-only fit to the control regions (described in the text). All statistical and systematic uncertainties are included.
background is normalised to match data in a b-veto control region. 9 Another dedicated validation sample is constructed to test the background prediction for tt produced with a Z boson that decays to two neutrinos, ttZ(→ νν). This process represents an irreducible background that becomes important for SRs with stringent requirements on kinematic variables, such as tN high or tN boost. The validation strategy is to select tt events produced in association with a photon, ttγ. This process closely resem- bles ttZ(→ νν) in terms of Feynman diagrams and kinematic properties when the vector boson p T is well above m Z . The event selection is based on one isolated lepton, four or more jets with at least one b-tag, one high-p T photon, as well as requirements on modified versions of m T and E miss T where photons are treated as invisible particles. Figure 12 (right) compares data and background predictions, illustrating the accuracy of data modelling. The sample of 104 events has a purity in ttγ of more than 70%. The production of ttγ events is estimated using simulation, based on the same generator (MadGraph) as used for the ttZ process, and normalised to the NLO theoretical cross-section [133].

Systematic uncertainties
The systematic uncertainties affecting the results can be divided into two classes: uncertainties due to theoretical predictions and modelling, and uncertainties stemming from experimental effects. The impact of both types of uncertainty is evaluated for all background and signal samples. Since the yields for the dominant background sources, tt and W +jets, are obtained in dedicated control regions, the modelling uncertainties for these processes affect only the extrapolation from the CRs into the signal regions (and between TCR and WCR), but not the overall normalisation. The systematic uncertainties are included as nuisance parameters and profiled in the likelihood fits. The nuisance parameters are constrained by Gaussian terms with widths corresponding to the sizes of the systematic uncertainties. The effects of the sources of uncertainties discussed in this section are quantified in terms of the corresponding relative uncertainty on the estimated number of background events in the various signal regions, this is referred to as the 'impact on the background estimate'.
The dominant experimental uncertainties arise from imperfect knowledge of the jet energy scale (JES) and jet energy resolution (JER) as well as from the modelling of the b-tagging efficiency. The JES uncertainty is derived from a combination of simulation and data samples [105,106] taking into account the dependence on the p T , η and flavour of the jet as well as the amount of pileup. The impact of JES on the background estimate varies from 1% to 13%. The JER uncertainties are determined with in-situ measurements of the jet response balance in dijet events [129], and the impact on the background estimate is 1%-21%. The JES, JER, and jet mass scale and resolution uncertainties for large-R jets are derived from a combination of data and simulation samples [107,134], and their combined impact on the background estimate amounts to 3%. The b-tagging uncertainty is estimated by varying the b-tagging efficiency and mis-tag rate correction factors, obtained from data-driven measurements of these quantities in tt and dijet events [111,[135][136][137], within their uncertainties. The impact of these uncertainties on the background estimate ranges from 1% to 8%, and is dominated by the uncertainty on the b-tagging efficiency. Other sources of experimental uncertainty are the modelling of the average number of pp interactions per bunch crossing, the modelling of the contribution to the E miss T from energy deposits not associated with any reconstructed objects and from pileup, the modelling of lepton-related quantities (trigger and identification efficiency, energy and momentum scale and resolution, isolation and τ -veto) as well as imperfect knowledge of the integrated luminosity. The combined impact of these sources on the background estimate is between 1% and 5%.
Uncertainties related to theoretical predictions and MC modelling are evaluated for all signal and background processes obtained entirely or partly from simulated events. The sources of uncertainty considered for both the tt and W +jets background processes are the variations of the renormalisation and factorisation scales by factors of 0.5 and 2.0 as well as PDF variations, which are studied following the PDF4LHC recommendations [138] comparing CT10 NLO, MSTW2008 NNLO and NNPDF21 100 [139] PDF error sets. For the tt background, the uncertainty on the hadronisation modelling is derived from a comparison between events generated with POWHEG and interfaced with PYTHIA for the shower model and those generated in the same way, but interfaced with Herwig+Jimmy [140]. Furthermore, the effect of the modelling of ISR and final-state radiation (FSR) is studied using samples of tt events generated with ACERMC with reduced and increased amounts of additional radiation (constrained by the measurement of ref. [141]). The impact of the tt modelling on the background estimate is 2%-6%. For the W +jets background, the effect of varying the number of partons used in the hard-scatter process is estimated by comparing samples generated with up to four extra partons to samples generated with up to five extra partons. The impact of merging matrix elements and parton showers is studied by varying the SHERPA scales related to the matching scheme. As the W +jets background is normalised in a region with a b-tag veto, additional uncertainties on the flavour composition of the W +jets events in the signal region, based on the uncertainties on the measurement of ref. [142] extrapolated to higher jet multiplicities, are applied in all regions requiring at least one b-tagged jet. The impact of the W +jets modelling on the background estimate is 1%-7%.
Background sources other than tt and W +jets are estimated from simulated events and are normalised to the most accurate cross-section predictions available. The cross-section uncertainty for the single-top process is 7% [82][83][84], while it is 22% for ttV [85,86]. The ZZ and W Z cross-section uncertainties are 5% and 7%, respectively [89,90]. Other sources of systematic uncertainty considered depend on the physics process, but include the choice of renormalisation and factorisation scales, PDF variations, hadronisation modelling, choice of MC generator, modelling of ISR and FSR, variations of the matrix element to parton shower matching scales, the generation of a finite number of partons, and the interference between single-top and tt production at NLO. The uncertainty on the interference treatment is estimated using inclusive W W bb samples at LO generated with ACERMC (which includes both the tt and W t processes). The total impact of the modelling of the smaller backgrounds on the background estimate ranges from 1% to 11%.
The theoretical uncertainties affecting the signal yields originate from the uncertainty on the production cross-section [96], and from the uncertainty on the acceptance. The latter includes PDF variations assessed using the PDF4LHC prescription [138], as well as modelling uncertainties of ISR and FSR and variations of the renormalisation and factorisation scales, evaluated by varying the relevant parameters in MadGraph. The total uncertainty on the production cross-section varies as a function of the stop mass; it amounts to about 15% for mt 1 = 200 GeV and increases to 18% for mt 1 = 700 GeV. The impact of the ISR/FSR modelling uncertainty on the signal acceptance ranges from 10% to 20% for signal regions that select events with ISR activity, such as bCc diag, and for signal models of mass hierarchy (c). It is negligible for the other signal regions.
The search sensitivity is directly connected to the fitted uncertainty of the signal strength parameter, where the signal strength is a fit parameter that scales the signal yield predicted by the model in question; a signal strength of one corresponds to the nominal signal yield. The impact of the various sources of uncertainty, including the statistical precision, on the signal strength uncertainty is quantified in table 10 for selected signal regions and signal benchmark models. The breakdown of the size of the systematic uncertainties is evaluated by re-running the fit, fixing the relevant nuisance parameter in question to its value from the nominal fit, and taking the difference in quadrature between the result of this fit and the nominal fit. The statistical uncertainty is obtained from rerunning the fit without any systematic uncertainties, again fixing the nuisance parameters to their values from the nominal fit. The tightest signal regions, such as tN boost, are statistically limited. Systematic uncertainties dominate the looser signal regions. Overall, the largest contributions to the systematic uncertainty on the signal strength come from JER and tt modelling. The energy scale and energy resolution of large-R jets is relevant in the tN boost signal region.   10 Results Table 11 shows the number of observed events together with the predicted number of background events in the 15 signal regions. For each of the four two-dimensional shapefits, numbers are given for the four bins with the largest expected signal-to-background ratios. For the selections with a one-dimensional shape-fit (bCa low, bCa med, bCb med1, bCb high), the listed numbers correspond to the cut-and-count 'discovery setup' selection (table 5). . The predicted numbers of background events are obtained using the background-only fits to the number of observed events in the CRs as described in section 8. These fitted background estimates in the CRs are then used to obtain the fitted numbers of background events in the signal regions by extrapolations that use transfer factors obtained with simulated events. The observed numbers of events are found to agree well with the fitted numbers of background events in all signal regions. Figures 13 and 14 show comparisons between the observed data and the SM background prediction from the background-only fit with all selections applied except the requirement on the plotted variable. The expected distributions from representative signal benchmark  Figure 13. For each signal region one characteristic distribution is shown, with the full event selection of the signal region applied, except for the requirement (indicated by an arrow) on the shown quantity. The uncertainty band includes statistical and all experimental systematic uncertainties. The last bin includes overflows. Benchmark signal models are overlaid for comparison. models are overlaid. The binning of the plots in figure 14 is similar to that used for the (one-dimensional) shape-fits of the corresponding signal regions.
To assess the compatibility of the SM background-only hypothesis with the observations in the signal regions, a profile likelihood ratio test, based on likelihood fits including one SR and all its associated CRs, is performed. Each SR, and each signal-sensitive bin in the shape-fits, is probed separately. For these tests, the event selection includes the -41 - 'discovery setup' requirement as described in tables 4-7. Table 11 shows the p 0 values obtained using these fits, indicating that the data in all signal regions are compatible with the background-only hypothesis. Good agreement is found when comparing the results obtained using pseudo-experiments to those calculated from asymptotic formulae [143]; the latter is used as the default for all exclusion results presented below.
As no significant excess over the expected background from SM processes is observed, the data are used to derive one-sided limits at 95% CL. The results are obtained from a profile likelihood ratio test following the CL s prescription [144]. Model-independent upper limits on beyond-SM contributions are derived separately for each signal region, and each signal-sensitive bin in the shape-fits. The likelihood of the fit is configured to include one SR or shape-fit bin and all its associated CRs. A generic signal model, which contributes only to the SR, is assumed and no experimental or theoretical signal systematic uncertainties are assigned other than the luminosity uncertainty. The event selection is the same as  Table 11. Columns two to four show the numbers of observed events in the eleven cut-and-count and four shape-fit signal regions together with the expected numbers of background events (as predicted by the background-only fits) and the probabilities, represented by the p 0 values, that the observed numbers of events are compatible with the background-only hypothesis. The p 0 values are obtained with pseudo-experiments with the exception of the shape-fit bins where only the smallest p 0 is derived with pseudo-experiments while the others are calculated from asymptotic formulae [143]. The p 0 value is set to 0.5 whenever the number of observed events is below the number of expected events. Columns five to eight show the 95% CL upper limits on the number of beyond-SM events (N non−SM ) and on the visible signal cross-section (σ vis = σ prod × A × ). The observed and (median) expected limits are given for a generic model without uncertainties other than on the luminosity. efficiency ( ) and production cross-section (σ prod ); it is obtained by dividing the upper limit on the number of beyond-SM events by the integrated luminosity.
-43 -Exclusion limits are also derived in various SUSY scenarios. The results are obtained using the same likelihood ratio test and fit as used for the generic limits, but including all shape-fit bins in the likelihood, and with the signal uncertainties and potential signal contributions to both the SRs and CRs taken into account. The 'exclusion setup' event selection is applied as described in tables 4-7. All uncertainties except on the theoretical signal cross-section are included in the fit. Combined exclusion limits are obtained by selecting a priori the signal region with the lowest expected CL s value for each signal grid point.
The expected and observed exclusion contours for thet 1 → tχ 0 1 decay mode are shown in figure 15 overlaying the results for the signal regions targeting two-, three-and fourbody decays. The ±1 σ exp uncertainty band indicates the impact on the expected limit of all uncertainties included in the fit. The ±1 σ SUSY theory uncertainty 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 cross-section uncertainty. Quoted limits are derived from the −1 σ SUSY theory observed limit contours. In the four-body scenario stop masses are excluded between 100 and 170 GeV, for an LSP mass of about 75 GeV. Stop masses between 100 and nearly 175 GeV in the three-body scenario, and between 210 and 640 GeV in the twobody scenario are excluded for a massless LSP, while for a stop mass around 550 GeV the exclusion reaches up to an LSP mass of 230 GeV. The non-excluded area between the fourand three-body decay regions is due to a reduction in search sensitivity as the kinematic properties of the signal change significantly when transitioning from a four-body to a three-body decay. In particular, approaching this boundary from the three-body side, the momenta of the two b-jets decrease to zero and hence the acceptance of the p T requirement on the b-tagged jet in the 3body signal region drops quickly. The kinematic properties change again at the other diagonal, between the three-body and on-shell top quark decay scenarios. When approaching this diagonal from the on-shell top quark side the search sensitivity is limited by the difficulty to disentangle the signal from the tt background, as the two processes begin to closely resemble each other in kinematic properties. In the limit of reaching the diagonal from the righthand side, the two LSPs have no phase space, thus carrying away no momentum, leading to a stop signature similar to that of tt except for small deviations induced by the difference in spin. This region is also referred to as 'stealth stop'. The tN diag signal region has the best expected sensitivity for stop masses up to 400 GeV and close to the mt ∼ 175 GeV is due to the same effect seen in figure 16 and described above, while the reduction in exclusion power for a decreasing LSP mass is due to the transition of theχ ± 1 decay from a three-body to a two-body process, which happens at an LSP mass of ∼ 26 GeV; the two-body decay produces less E miss T on average, amongst other changes of the kinematic properties.  is illustrated by fixing the stop mass to 300 GeV and presenting the exclusion limit as a function of theχ  figure 25. The strongest impact on the CL s significance is found to be from the sum of the branching ratios fort 1 → tχ 0 1 andt 1 → bχ ± 1 , where the CL s significance is smaller for models where stop decays other thant 1 → tχ 0 1 andt 1 → bχ ± 1 are kinematically allowed. This is a consequence of the signal selections being optimised using only simplified models. In addition to the branching ratio dependence, the sensitivity also depends on the kinematic properties of the events, which are affected, e.g., by the stop mixing matrix and by the masses and field content of other SUSY particles. These additional dependencies explain the large spread in CL s significance for the models where the stop decays only to tχ

Summary and conclusions
A search for stop pair production in final states with one isolated lepton, jets, and missing transverse momentum is presented. Proton-proton collision data from the full 2012 datataking period were analysed, corresponding to an integrated luminosity of 20 fb 1 the decay of thet 1 involves a virtual top quark (three-body decay), while in the region mt 1 < m b + m W + mχ0 1 it involves both a virtual top quark and a virtual W boson (four-body decay). The mt 1 < 100 GeV region for the three-body decay scenario is excluded by the search described in ref. [38]. Furthermore, the mt 1 < 78 GeV region in the four-body scenario is excluded by the search in ref. [145].
(1) each stop decays to a top quark and the LSP; (2) each stop decays to a bottom quark and the lightest chargino (χ ± 1 ), where theχ ± 1 decays via an on-or off-shell W boson to the LSP; (3) each stop decays in a three-body process to a bottom quark, a W boson, and the LSP; (4) each stop decays in a four-body process to a bottom quark, the LSP and two light fermions; (5) the two stops decay independently either as described in (1) or in (2). In all scenarios, R-parity is conserved and the LSP is assumed to be theχ           -54 - -57 -

A Detailed description of the discriminating variables
This section provides more detailed descriptions of the discriminating variables that are introduced in section 6.
-Stransverse Mass, m T2 This variable targets decay topologies with two branches, referred to here as a and b. In each branch, there are some particles with fully measured momenta and some particles with momenta that are not measured directly. The sum of the four vectors of the measured momenta in branch i ∈ {a, b} are denoted p i = (E i , p Ti , p zi ) and the sum of the four vectors of the unmeasured momenta are denoted q i = (F i , q Ti , q zi ). With i , the m T of the particles in branch i is given in general by which in the case that m q i = m p i = 0 is the same as the one given in section 6.2. A generalisation of m T , m T2 , is defined as a minimisation over the allocation of p miss T between q Ta and q Tb of the maximum of the corresponding m Ta or m Tb : where one must make an assumption of m qa and m q b in the computation of m T a and m T b . The result of the above minimisation is the minimum parent mass consistent with the observed kinematic distributions under the inputs m qa and m q b . The variants of m T2 described below only differ in the measured particles, (assumed) unmeasured particles, and choices for the input masses, m qa and m q b .
-Asymmetric m T2 , am T2 -Measured particles: For branch a, this is one of the b-jets and for branch b this is the second b-jet and the charged lepton. The b-jets are identified based on the highest b-tagging weights. Since there are two ways of assigning the b-tagged jets to branches a and b, both m T2 values are computed and the minimum kept for the final discriminant.
-Unmeasured particles: For branch a, this is a W boson that decays leptonically, with the charged lepton unidentified as such. The unmeasured particle for branch b is the neutrino associated with the measured charged lepton.
-τ -based m T2 , m τ T2 -63 --Measured particles: For branch a, this is the τ -jet, identified as the highest-p T jet excluding the selected two b-tagged jets. The measured particle for branch b is the charged lepton.
-Unmeasured particles: For branch a, this includes the two neutrinos associated with the τ production and hadronic decay. The unmeasured particle for branch b is the neutrino associated with the charged lepton.

-Topness
The topness event value is defined as ln(minŜ), whereŜ is the minimum of the χ 2 -type function S: The first three arguments of S are the components of the non-reconstructed W boson 3momentum (p W,x , p W,y , p W,z ). This W is assumed to decay leptonically, but the lepton is not reconstructed and is thus only noticeable in the missing transverse momentum. The variable p ν,z is the longitudinal momentum of the neutrino from the other W boson decay, for which the lepton was successfully reconstructed. These four numbers are varied to find the minimum of S.
The momenta appearing on the right-hand side of the equation above are either 4momenta of the reconstructed objects (one lepton, p , and two b-jets, p b 1 and p b 2 ) or 4-momenta assigned by the minimisation procedure (p W and p ν ). To find all four components, the neutrinos and the W boson without reconstructed decay products are assumed to be on-shell. Both combinations for b 1 and b 2 are evaluated during the minimisation; if only one b-tagged jet is present, it is used together with the leading or subleading jet (that means, a total of four possible jet assignments is evaluated in this case).
The minimisation is constrained such that the observed missing transverse momentum is attributed to the unobserved W boson (decaying into a not-reconstructed lepton and a neutrino) and a neutrino from the other top decay branch.
The constants a W , a t and a CM are set to the values suggested by the authors of S: a W = 5 GeV, a t = 15 GeV, a CM = 1 TeV.
-Hadronic top mass, m had−top This reconstructed top mass is constructed as m j 1 ,j 2 ,b i by minimising where i = 1 or 2; b 1 and b 2 are the two jets with the highest b-tagging weights; j 1 , j 2 are the highest p T jets from the selected jets in the event excluding b 1 and b 2 and where r i is the fractional jet energy uncertainty of the p T for jet i determined by dedicated studies [105,129].