Search for top squarks in final states with one isolated lepton, jets, and missing transverse momentum in $\sqrt{s}=13$ TeV $pp$ collisions with the ATLAS detector

The results of a search for the stop, the supersymmetric partner of the top quark, in final states with one isolated electron or muon, jets, and missing transverse momentum are reported. The search uses the 2015 LHC $pp$ collision data at a center-of-mass energy of $\sqrt{s}=13$ TeV recorded by the ATLAS detector and corresponding to an integrated luminosity of 3.2 fb${}^{-1}$. The analysis targets two types of signal models: gluino-mediated pair production of stops with a nearly mass-degenerate stop and neutralino; and direct pair production of stops, decaying to the top quark and the lightest neutralino. The experimental signature in both signal scenarios is similar to that of a top quark pair produced in association with large missing transverse momentum. No significant excess over the Standard Model background prediction is observed, and exclusion limits on gluino and stop masses are set at 95% confidence level. The results extend the LHC Run-1 exclusion limit on the gluino mass up to 1460 GeV in the gluino-mediated scenario in the high gluino and low stop mass region, and add an excluded stop mass region from 745 to 780 GeV for the direct stop model with a massless lightest neutralino. The results are also reinterpreted to set exclusion limits in a model of vector-like top quarks.


Introduction
Supersymmetry (SUSY) [1][2][3][4][5][6] is a natural solution [7,8] to the hierarchy problem [9][10][11][12]. The top squark or stop (t), which is the superpartner of the top quark, is expected to be relatively light due to its large contribution to the Higgs boson mass radiative corrections [13,14]. For reasons such as gauge unification [15] and the two-loop radiative corrections to the Higgs boson mass [16,17], one may also expect a TeV mass scale for the gluino (g), the superpartner of the gluon. A common theoretical strategy for avoiding strong constraints from the nonobservation of proton decay [18] is to introduce a multiplicative quantum number called R-parity. If R-parity is conserved [19], SUSY particles are produced in pairs and the lightest supersymmetric particle (LSP) is stable. This analysis follows the typical assumption that the lightest neutralino 1 (χ 0 1 ) is the LSP. Since theχ 0 1 interacts only weakly, it can serve as a candidate for dark matter [20,21]. This paper presents a search targeting the lighter stop 2 (t 1 ) in two scenarios: gluino-mediated pair production of thet 1 with a smallt 1 -LSP mass splitting, and direct pair production of thet 1 , both illustrated by the diagrams in Fig. 1. The former scenario refers to pair production of gluinos, each decaying to the top quark and thet 1 . In this scenario, the mass difference between the gluino and thẽ t 1 is assumed to be well above the top quark mass, while the mass difference between thet 1 and the LSP is assumed to be significantly smaller than the W boson mass. As a result, the visiblet 1 decay products have low momentum, typically below the reconstruction and identification thresholds. This scenario is motivated by the dark matter relic density, which is generally too large in the Minimal Supersymmetric Standard Model [22,23] but can be regulated by coannihilation of the stop and the neutralino [24]. In the second scenario, the two directly producedt 1 are each assumed to decay to the top quark and the LSP. This model is interesting as it is independent of the gluino mass, which is more weakly constrained by naturalness arguments than the stop mass.
Experimentally, the final states of the two scenarios are similar [25], and the detector signature consists of the decay products of a pair of top quarks 3 and large missing transverse momentum ( p miss T , where the magnitude is referred to as E miss T ) from the two LSPs: tt + E miss T . The main difference between the two scenarios is that the production cross-section for gluino pairs is about a factor 50 higher than for t 1 pairs of the same mass due to the additional spin and color states. The results are also reinterpreted in a model of strong-interaction direct pair production of vector-like top quarks T (referred to as VLQ) [26][27][28], for which the decay mode T → tZ with Z → νν has a signature similar to that of direct stop pair production witht 1 → tχ 0 1 .
The analysis presented here -which is based on previous ATLAS searches for the same signature [29, 30] -targets the one-lepton final state where the W boson from one of the top quarks decays to an electron or muon (either directly or via a τ lepton) and the W boson from the other top quark decays hadronically. The dominant Standard Model (SM) background processes are: the production of tt ; the associated production of a top quark and a W boson (single top Wt); tt + Z(→ νν); and the associated production of W bosons and jets (W+jets). The search uses the ATLAS data collected in 1 The charginosχ ± 1,2 and neutralinosχ 0 1,2,3,4 are the mass eigenstates formed from the linear superposition of the charged and neutral SUSY partners of the Higgs and electroweak gauge bosons (higgsinos, winos and binos). 2 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 is the lighter one. 3 Due to the Majorana nature of the gluino, in the gluino-mediated model, each of the two 'visible' top quarks can independently be a top or an antitop quark. Hereafter, the term tt can be taken to refer to any combination of t andt. proton-proton (pp) collisions in 2015 corresponding to an integrated luminosity of 3.2 fb −1 at a centerof-mass energy of √ s = 13 TeV. The ATLAS Run-1 searches for gluino-mediated stop production and direct stop pair production are summarized in Refs.
This document is organized as follows. The ATLAS detector, dataset, and trigger are described in Section 2, and the corresponding set of simulations are detailed in Section 3. Section 4 presents the reconstruction and selection of physics objects and the construction of discriminating variables. These variables are used in Section 5 to construct the signal event selections. The background estimation procedure (Section 6) and systematic uncertainties (Section 7) are described before the results are presented in Section 8. Section 9 contains concluding remarks.

ATLAS Detector and Dataset
The ATLAS detector [44] is a multipurpose particle physics detector with nearly 4π coverage in solid angle around the collision point. 4 It consists of an inner tracking detector (ID), surrounded by a superconducting solenoid providing a 2 T axial magnetic field, a system of calorimeters, and a muon spectrometer (MS) incorporating three large superconducting toroid magnets. The ID provides charged-particle tracking in the range |η| < 2.5 using three technologies: silicon pixel and silicon microstrip tracking detectors, and a transition radiation tracker. During the LHC shutdown between Run 1 and Run 2, a new innermost layer of silicon pixels was added, which improves the track impact parameter resolution and vertex position resolution [45]. High-granularity electromagnetic and hadronic 4 ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the center of the detector and the z-axis along the beam pipe. The x-axis points from the IP to the center of the LHC ring, and the y-axis points upwards. Cylindrical coordinates (r, φ) are used in the transverse plane, φ being the azimuthal angle around the z-axis. The pseudorapidity is defined in terms of the polar angle θ as η = − ln tan(θ/2). Angular distance is measured in units of ∆R ≡ (∆η) 2 + (∆φ) 2 .
calorimeters cover the region |η| < 4.9. The central hadronic calorimeter is a sampling calorimeter with scintillator tiles as the active medium and steel absorbers. All the electromagnetic calorimeters, as well as the endcap and forward hadronic calorimeters, are sampling calorimeters with liquid argon as the active medium and lead, copper, or tungsten absorber. The MS consists of three layers of highprecision tracking chambers with coverage up to |η| = 2.7 and dedicated chambers for triggering in the region |η| < 2.4. Events are selected by a two-level trigger system: the first level is a hardware-based system and the second is a software-based system.
The 2015 LHC collision data used in this analysis has a mean number of additional pp interactions per bunch crossing (pileup) of approximately 14, and a bunch spacing of 25 ns. Following requirements based on beam and detector conditions and data quality, the dataset corresponds to an integrated luminosity of 3.2 fb −1 with an associated uncertainty of 5%. The uncertainty is derived following the same methodology as that detailed in Ref. [46]. Events used for this search were recorded using a trigger logic that accepts events with E miss T , calibrated to the electromagnetic scale, above 70 GeV. The trigger is more than 95% efficient for events passing an offline-computed E miss T > 200 GeV requirement and is > 99% efficient for events passing all signal selections. An additional data sample used to estimate one of the background processes was recorded with a trigger requiring a photon with transverse momentum p T > 120 GeV, which is > 99% efficient for the offline photon selection described in Section 4.

Monte Carlo Simulations
Samples of Monte Carlo (MC) simulated events are used for the description of the background and to model the SUSY signals. Several matrix element (ME) generators are combined with parton shower (PS) and hadronization generators. Signal SUSY samples are generated at leading order (LO) with MG5_aMC 2 [47] while VLQ signal samples are generated at LO with Protos v2.2 [48,49]. All signal samples are interfaced with Pythia 8.186 [50]. Background samples use one of three setups: • MG5_aMC v2 interfaced with Pythia 8 or Herwig++ using the CKKW-L [51] or the MC@NLO method for matching a LO or next-to-leading-order (NLO) ME to the PS, respectively.
• Sherpa 2.1.1 [60] using Comix [61] and OpenLoops [62] ME generators interfaced with the Sherpa parton shower [63].  In the gluino-mediated production the stop is assumed to decay viat 1 → c+χ 0 1 with a 100% branching ratio and with a default mass splitting mt 1 − mχ0 1 = 5 GeV. Alternative samples with larger mass splitting and/or replacing the two-body stop decay by a four-body stop decayt 1 → b f f χ 0 1 , where f f is a fermion-antifermion pair, are produced for additional studies. The gluinos and stops are assumed to decay promptly. In the direct stop pair production samples, thet 1 is chosen to be mostly the partner of the right-handed top quark 5 and theχ 0 1 to be a pure bino. This choice is consistent with a large branching ratio for the givent 1 decay. Different hypotheses for 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 polarization 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. Signal grids are generated for both the gluino and direct stop pair production models. The spacing between grid points in the gluino-stop and stop-neutralino mass planes vary between 25 and 100 GeV.
All the MC samples are normalized to the highest-order (in α S ) cross-section available, as indicated in the last column of Table 1. The cross-sections for the pair and single production of top quarks as well as for the signal processes also include resummation of soft gluon emission to next-to-next-to-leadinglogarithmic (NNLL) and next-to-leading-logarithmic (NLL) accuracy, respectively. As is described in Section 6.1.3, it is important that the simulated tt + γ and tt + Z events are as similar as possible. Therefore, a small 4% correction is applied to the tt+γ cross-section to account for a different PDF set, factorization/renormalization scale, and number of partons from the matrix element. 6 The same NLO QCD K-factor is then applied to the tt + γ process as is used for the tt + Z(→ νν) process [47]. This choice is motivated by the similarity of QCD calculations for the two processes as well as empirical studies of the ratio of K-factors computed as a function of the boson p T . Further information about the K-factor and its uncertainty is given in Section 7. The cross-sections for the tt, W+jets, and Wt 5 Thet R component is given by the the off-diagonal entry of the stop mixing matrix. Thet 1 decays in the direct stop pair production samples are performed by Pythia and produce unpolarized top quarks. The events are reweighted to obtain a stop mixing equivalent to a matrix with on-diagonal entries of approximately 0.55 and off-diagonal entries of approximately ±0.83. The event weights depend on the angular distributions of the top decay products [86]. 6 The tt + γ sample uses a fixed factorization/renormalization scale of 2 × m top with no extra partons in the ME. The tt + Z sample uses the default m T scale and is generated with up to two partons. The top decay is performed in MG5_aMC for tt + γ to account for hard photon radiation from the top decay products, which is a ∼ 15% effect for p γ T ∼ 120 GeV [87].
processes are used for cross-checks and optimization studies, while for the final results these processes are normalized to data in control regions.
All background samples, except for the tt + γ sample, are processed with the full simulation of the ATLAS detector [88] based on Geant 4 [89]. The signal samples and the tt + γ sample are processed with a fast simulation [90] of the ATLAS detector with parameterized showers in the calorimeters. All samples are produced with varying numbers of simulated minimum-bias interactions generated with Pythia 8 overlaid on the hard-scattering event to account for pileup from multiple pp interactions in the same or nearby bunch crossings. The average number of interactions per bunch crossing is reweighted to match the distribution in data. Furthermore, the simulated samples are reweighted to account for small differences in the efficiencies of physics-object reconstruction and identification with respect to those measured in data.

Event Reconstruction and Selection
All events must satisfy a series of quality criteria before being considered for further use. The reconstructed primary vertex with the highest tracks p 2 T must have at least two associated tracks. In this analysis, physics objects are labeled as either baseline or signal depending on various quality and kinematic requirements, where the latter label describes a tighter selection of the former. Baseline objects are used to distinguish between the physics objects in the event and to compute the missing transverse momentum. Baseline leptons (electrons and muons) are also used to apply a second-lepton veto to suppress dilepton tt and Wt events.
Electron candidates are reconstructed from electromagnetic calorimeter cell clusters that are matched to ID tracks. Baseline electrons are required to have p T > 7 GeV, |η| < 2.47, and satisfy 'VeryLoose' likelihood identification criteria that are defined following the methodology described in Ref. [91]. Signal electrons must pass all baseline requirements and in addition have p T > 25 GeV, satisfy the 'Loose' likelihood identification criteria in Ref. [91], and have impact parameters with respect to the reconstructed primary vertex along the beam direction (z 0 ) and in the transverse plane (d 0 ) that satisfy |z 0 sin θ| < 0.5 mm and |d 0 |/σ d 0 < 5, where σ d 0 is the uncertainty of d 0 . Furthermore, signal electrons must be isolated, where the criteria use track-based information to obtain a 99% efficiency that is independent of p T , as derived from Z → MC samples and confirmed in data.
Muons are reconstructed from combined tracks that are formed from ID and MS tracks, ID tracks matched to MS track segments, standalone MS tracks, or ID tracks matched to an energy deposit in the calorimeter compatible with a minimum-ionizing particle (referred to as calo-tagged muon) [92]. Baseline muons are required to have p T > 6 GeV, |η| < 2.7, and satisfy the 'Loose' identification criteria described in Ref. [92]. Signal muons must pass all baseline requirements and in addition have p T > 25 GeV, and have impact parameters |z 0 sin θ| < 0.5 mm and |d 0 |/σ d 0 < 3. Furthermore, signal muons must be isolated according to isolation criteria similar to those used for signal electrons, yielding the same efficiency.
Photon identification is not used in the main event selection, and photons give rise to extra jet or electron candidates. Photons must be identified, however, for the tt + γ sample that is used in the data-driven estimation of the tt + Z background. In this case, photon candidates are reconstructed from calorimeter cell clusters and are required to satisfy the 'Tight' identification criteria described in Ref. [93]. Furthermore, photons are required to have p T > 125 GeV and |η| < 2.37, excluding the barrel-endcap calorimeter transition in the range 1.37 < |η| < 1.52, so that the photon trigger is fully efficient. Photons must further satisfy isolation criteria based on both track and calorimeter information.
Jet candidates are built from topological clusters [94,95] in the calorimeters using the anti-k t algorithm with a jet radius parameter R = 0.4 [96]. Jets are corrected for contamination from pileup using the jet area method [97-99] and then calibrated to account for the detector response [100, 101]. Jets in data are further calibrated based on in situ measurements of the jet energy scale. Baseline jets are required to have p T > 20 GeV. Signal jets must have p T > 25 GeV and |η| < 2.5. Furthermore, signal jets with p T < 50 GeV are required to satisfy criteria, implemented in the jet vertex tagger algorithm [99], designed to reject jets originating from pileup. Events containing a jet that does not pass specific jet quality requirements are vetoed from the analysis in order to suppress detector noise and noncollision backgrounds [102,103]. Jets resulting from b-quarks (called b-jets) are identified using the MV2c20 b-tagging algorithm, which is based on quantities such as impact parameters of associated tracks and reconstructed secondary vertices [104][105][106]. This algorithm is used at a working point that provides 77% b-tagging efficiency in simulated tt events. The choice of working point was optimized for this analysis and corresponds to a rejection factor of about 140 for light-quark flavors and gluons and about 5 for charm jets. Jets and associated tracks are also used to identify hadronically decaying τ leptons using the 'Loose' identification criteria described in Refs. [107, 108], which have a 60% and 50% efficiency for reconstructing τ leptons decaying into one and three charged pions, respectively. These τ candidates are required to have one or three associated tracks, with total electric charge opposite to that of the selected electron or muon, p T > 20 GeV, and |η| < 2.5. This τ candidate p T requirement is applied after a dedicated energy calibration [108].
The missing transverse momentum is reconstructed from the negative vector sum of the transverse momenta of baseline electrons, muons, jets, and a soft-term built from high-quality tracks that are associated with the primary vertex but not with the baseline physics objects [109,110]. For the event selections requiring photons, the calibrated photon is directly included in the E miss T calculation. In all other cases, photons and hadronically decaying τ leptons are not explicitly included but enter as jets or electrons, or via the soft-term.
To avoid labeling the same detector signature as more than one object, an overlap removal procedure is applied. The procedure is tailored for this analysis and optimized using simulation. Table 2 summarizes the procedure. Given a set of baseline objects, the procedure checks for overlap based on a minimal distance ∆R between pairs of objects. For example, if a baseline electron and a baseline jet are found with ∆R < 0.2, then the electron is retained (as stated in the 'Precedence' row) and the jet is discarded, unless the jet is b-tagged (as stated in the 'Condition' row) in which case the electron is assumed to stem from a heavy-flavor decay and is hence discarded while the jet is retained. If the '∆R<' requirement in Table 2 is not met, then both objects under consideration are kept. The order of steps in the procedure is given by the columns in Table 2, which are executed from left to right. The second (e j) and the third (µ j) steps of the procedure ensure that leptons and jets have a minimum ∆R separation of 0.2. Therefore, the fourth step ( j) only has an effect for ∆R > 0.2. The steps involving a photon are not applied in the main event selection, but only for the event selection where photons are identified. For the remainder of the paper, all baseline and signal objects are those that have survived the overlap removal procedure.
Large-radius jets are clustered from all signal (small-radius R = 0.4) jets using the anti-k t algorithm with R = 1.0 or 1.2. To reduce the impact of soft radiation and pileup, the large-radius jets are groomed using reclustered jet trimming, where constituents with p T less than 5% of the ungroomed jet p T are Precedence e e µ j γ e e Table 2: Overlap removal procedure. The first two rows list the types of overlapping objects: electrons (e), muons (µ), electron or muon ( ), jets ( j), photons (γ), and hadronically decaying τ lepton (τ). All objects refer to the baseline definitions, except for γ and τ where no distinction between baseline and signal definition is made. The third row specifies when an object pair is considered as overlapping, the fourth row describes an optional condition, and the last row lists which label is given to the ambiguous object. More information is given in the text.
removed [111][112][113][114]. Electrons and muons are not included in the reclustering, since it was found that including them increases the background acceptance more than the signal efficiency. Large-radius jets are not used in the overlap removal procedure; however, the signal jets that enter the reclustering have passed the overlap removal procedure described above. The analysis uses a large-radius jet mass, where the squared mass is defined as the square of the four-vector sum of the constituent (small-radius) jets' momenta.
All events are required to have E miss T > 200 GeV, exactly one signal lepton, and no additional baseline leptons, as well as at least four signal jets. In addition, the events must have a transverse mass 7  is computed using the per-event jet energy resolution uncertainties (more details are given in Refs. [29,115]). The latter three event selection criteria for m T , |∆φ(jet i , p miss T )|, and H miss T,sig suppress multijet processes with misidentified or nonprompt leptons and mismeasured E miss T to a negligible level. With the above event selection, the dominant backgrounds are tt events with at least one leptonically decaying W boson, and W+jets production. A powerful technique for suppressing these background processes is to require m T to be greater than the W boson mass. For example, an m T > 120 GeV requirement removes more than 90% of tt and W+jets events that pass the above event selection.
One of the dominant contributions to the residual background is from tt production where both W bosons decay leptonically, or one W boson decays leptonically and the other via a hadronic τ decay. A series of additional variables, described in detail in Ref. [29], are used to discriminate between this background and the signal processes. The m transverse mass applied to signatures where two particles are not directly detected. The am T2 variable targets dileptonic tt events where one lepton is not reconstructed, while the m τ T2 variable targets tt events where one of the two W bosons decays via a hadronically decaying τ lepton. The topness [121] variable is based on minimizing a χ 2 -type function quantifying the compatibility with a dileptonic tt event where one lepton is not reconstructed. Furthermore, the mass of large-radius jets is useful when the boost of the top quark is significant.
An important change from the Run-1 suite of tools is the treatment of hadronically decaying τ candidates in the m τ T2 variable. Events are removed if one of the selected jets is additionally identified as a hadronic τ candidate, with a corresponding m τ T2 < 80 GeV, where m τ T2 uses the signal lepton and hadronic τ candidate as the two visible objects. For an event selection with a E miss T > 200 GeV requirement, this hadronic τ veto removes approximately 40% of simulated tt events where one W boson decays leptonically and the other decays via a hadronically decaying τ lepton. For the considered signal models, the veto removes 1% of the events. The τ veto is applied in all following event selections except those defining the tt + Z control region (since the veto would remove only about 1% of the events in this region).

Signal Regions
Three signal event selections (called signal regions, or SR1-3) are constructed using the set of discriminating variables described in Section 4. The three signal regions are optimized, before looking at the data, to maximize the discovery sensitivity using three benchmark signal models from the gluino-mediated stop models, each representing a distinct phenomenology. The benchmark models are defined by (g,χ 0 1 ) masses of (1100, 800), (1250, 750), and (1400, 400) GeV for SR1, SR2, and SR3, respectively. The benchmark model for SR1 has a production cross-section and kinematic properties similar to those of a direct stop model with (t 1 ,χ 0 1 ) masses of about (600, 260) GeV, while the benchmark models for SR2 and SR3 cannot be directly mapped to have both the same cross-sections and similar kinematic properties. As a consequence, SR2 and SR3 have reduced sensitivity to direct stop models.
The three signal regions are characterized by increasing E miss T requirements. The SR1 benchmark has the softest E miss T spectrum and the momentum of the hadronically decaying top quark is typically not sufficient to capture all of the decay products inside a single large-radius jet. As a result, the top quark mass computed using the m χ top variable which is based on small-radius jets is useful for rejecting dileptonic tt and other background events without a top quark that has hadronic decay products. In contrast, the boost of the hadronically decaying top quarks in the SR2 and SR3 benchmarks is often sufficient to capture all decay products inside a single large-radius jet. The angular separation between the decay products scales with the inverse of the momentum. Therefore, the optimal large-radius jet cone size is found to be larger for SR2 (R = 1.2) than for SR3 (R = 1.0). Additional requirements on topness and am T2 further reduce the dileptonic tt background. Background events without a highp T top quark that decays leptonically are suppressed by using a requirement on the ∆R between the highest-p T b-tagged jet and the signal lepton. The signal regions have additional requirements on the m T and H miss T,sig variables to further exploit the large genuine E miss T from undetected neutralinos. A requirement of at least one b-tagged jet is used in each of SR1-3 in order to reduce the W+jets and diboson backgrounds.
The signal region definitions are summarized in Table 3. The signal regions are not mutually exclusive.

Background Estimates
The dominant background processes are tt, single top Wt, tt + Z(→ νν), and W+jets. Most of the tt and Wt events in the signal regions have both W bosons decay leptonically (one of which is 'lost', meaning it is either not reconstructed, not identified, or removed by the overlap removal procedure) or one W boson decays leptonically and the other via a hadronically decaying τ lepton. Other background processes considered are semileptonic tt, dibosons (denoted by VV in figure legends), tt + W, Z+jets, and multijet events. The tt background is shown separately in the three decay components discussed above, which are referred to as 2L, 1L1τ, and 1L respectively. 8 The combined tt +W and tt +Z background is referred to as tt +V.
The main background processes are estimated by isolating each of them in a dedicated control region (CR), described in Section 6.1, normalizing simulation to match data in a simultaneous fit. The fit is performed separately for each SR with the associated CRs. The background modeling as predicted by the fits is tested in a series of validation regions (VR), discussed in Section 6.2. Figure 2 schematically illustrates the setup for one example SR and its associated CRs and VRs. The CRs for Wt and tt + Z are new with respect to the Run-1 analysis.
The multijet background is estimated from data using a fake-factor method [122]. The contribution is found to be negligible. All other (small) backgrounds are determined from simulation, normalized to the most accurate theoretical cross-sections available. The Z+jets background is found to be negligible.

Control Regions
A series of control regions are defined as event selections that are kinematically close to the signal regions but with a few key variable requirements inverted to significantly reduce signal contamination and enhance the yield and purity of a particular background. These control regions are then used to constrain the background normalization. Each of the three signal regions has a dedicated control region for each of the following background processes: tt (TCR), W+jets (WCR), single top (STCR), and tt+W/Z (TZCR). The general strategy in constructing the control regions is to invert the transverse mass requirement from a high threshold to a low window. The requirements on several variables are loosened to increase the statistical power of the CR. The details of the TCR and the WCR are described in Section 6.1.1, while the STCR and TZCR are documented in Section 6.1.2 and 6.1.3 respectively. Table 3 presents an overview of the CR selections for the TCR, WCR, and STCR corresponding to SR1, SR2, and SR3. strength parameter to normalize the cross-section of a given signal model can be included in the fit. Each fit is based on up to five observables: the total yields in four control regions, and the total yield in one signal region. The electron and muon channels are always added together. To obtain a set of background predictions that are independent of the observations in the SRs, the fit can be configured to use only the CRs to constrain the fit parameters: the SR bins are removed from the likelihood and any potential signal contribution is neglected everywhere. This fit configuration is referred to as the background-only fit.

Top and W CRs
The TCRs and WCRs are constructed by modifying the m T selection in the SRs to be a window whose upper edge is near the W boson mass. An additional upper bound on am T2 is applied to the TCRs in order to make them orthogonal to the STCRs, described in the next section. Furthermore, some other kinematic requirements are relaxed or removed to increase the event yields in the CRs. The resulting selections yield 238, 102, and 121 events in TCR1, TCR2, and TCR3, respectively, which are enriched in semileptonic tt events with purities that vary between 75% and 85%. The WCRs are built from the TCRs by changing the b-jet requirement to a b-jet veto, and relaxing the am T2 requirement. The b-jet veto suppresses tt events and results in a W+jets purity of approximately 75% in all three regions. The selections yield 558, 135, and 352 events in WCR1, WCR2, and WCR3, respectively.

Single Top CR
All of the expected single-top contributions in the three SRs are in the Wt channel. This process can evade kinematic bounds from selections targeting the suppression of tt.
Nonetheless, isolating a pure sample of Wt events kinematically close to the SRs is challenging due to the similarity of Wt and tt. The Wt events that pass event selections similar to those for the SRs often have a second b-jet within the acceptance. The am T2 variable is useful for discriminating between tt and Wt because the mass of the Wb system not from the resonant top quark is typically higher than for an on-shell top quark in the phase space selected by this analysis. Therefore, the STCRs are characterized by am T2 > 200 GeV. Furthermore, to increase the purity of Wt and reduce the W+jets contamination, events are required to have two b-tagged jets. Top quark pair events often exceed the am T2 kinematic bound when one of the two b-tags used in the am T2 calculation is a jet produced from a charm quark from the W decay. When this jet is from the same top quark as the other b-tagged jet, the ∆R between them tends to be smaller than for Wt events that have two b-jets from b-quarks that are naturally well separated. Therefore, to further increase the Wt purity, events in the STCRs are required to have ∆R(b 1 , b 2 ) > 1.2 where b 1 and b 2 are the two highest-p T b-tagged jets. Figure 3 shows distributions of the key variables for STCR1 with all requirements applied except for that on the quantity plotted. The expected purity for Wt events is approximately 40% in all three STCRs, and the selections yield 62, 71, and 45 events in STCR1, STCR2, and STCR3, respectively.

tt + Z CR
Top quark pair production in association with a Z boson that decays into neutrinos is an irreducible background. The expected contributions of tt + W in the three SRs are less than 10% with respect to the expected tt + Z yields, and the two processes are combined in the analysis. A CR using Z boson decays to charged leptons is not feasible given the small branching ratio to leptons and the limited dataset available. However, a data-driven approach is still possible using a similar process: tt + γ. Similar techniques have been used for estimating Z(→ νν)+jets from γ+jets [124] and the method was studied as a VR in the direct stop search with one lepton with Run-1 data [29]. An event selection is constructed requiring a high-p T photon that is then treated as E miss T in direct analogy to Z → νν.
The CR is designed to minimize the differences between the two processes, in order to reduce the theoretical uncertainties in the extrapolation. The Feynman diagrams for the production of tt + Z and tt + γ are identical, except for a negligible production contribution where the Z boson is radiated from a neutrino (the coupling is absent for photons). The main differences arise from the Z boson mass, which reduces the available phase space, causing differences in kinematic distributions. In addition, the bremsstrahlung rate for Z bosons is highly suppressed at LHC energies, while there is a large contribution to the tt + γ cross-section from photons radiated from the top quark or its decay products. Both of these differences are mitigated if the boson p T is larger than the Z boson mass. In this limit, the impact of the mass difference on the available phase space is reduced and the rate of photon radiation from bremsstrahlung is suppressed [87]. This small fraction of photons is fully accounted for in the simulation and any uncertainty in their modeling is subdominant compared to the uncertainties described in Section 7. In high-E miss T tt + Z(→ νν) events, the Z boson p T is the dominant source of E miss T and so most tt + Z events in the SRs have large Z boson p T .   Table 4. The uncertainty band includes statistical and all experimental systematic uncertainties. The last bin includes overflow.
Two tt + γ CRs are designed to be kinematically close to SR1 and SR2/SR3. The event selection for TZCR2 is the same as for TZCR3. Both regions require at least one signal photon, exactly one signal lepton and no additional baseline leptons, and at least four signal jets, of which at least one must be b-tagged. The two regions have the same jet p T thresholds as the corresponding signal regions. To mimic the Z → νν decay, the highest-p T photon is vectorially added to p miss T and this sum is used to constructẼ miss T = | p miss T + p γ T |,m T , andH miss T,sig . Events entering the TZCRs are required to satisfỹ E miss T > 120 GeV,m T > 100 GeV, andH miss T,sig > 5 in order to bring the region kinematically closer to the SRs. Finally, E miss T < 200 GeV is imposed to ensure orthogonality between the TZCR and the other CRs and SRs. The resulting regions have over 90% tt + γ purity, and yield 43 and 45 events in TZCR1 and TZCR2 (=TZCR3), respectively. Figure 4 shows the distribution ofẼ miss T andm T in the TZCR1 corresponding to SR1 before the requirement on the plotted variable is applied. The contribution from events not involving top quarks is negligible. The predicted backgrounds in the figure are scaled with the NFs documented in Table 4. Without scaling, the total number of events in data is about 40% higher than in simulation, but there is no significant evidence of mismodeling of the shapes of the various distributions within uncertainties.

Validation Regions
The background estimates are tested using validation regions, which are disjoint to both the control and signal regions. Background normalizations determined in the control regions are extrapolated to the VRs and compared with the observed data. Each signal region has associated validation regions for the tt (TVR) and W+jets (WVR) processes, and these are constructed with the same selection as the TCR/WCR except that m T is between 90 and 120 GeV. 9 The validation regions are not used to constrain parameters in the fit, but provide a statistically independent test of the background estimates made using the CRs. In Fig. 5, background estimates in all the associated VRs are compared to the observed data. The potential signal contamination in the VRs is studied for all considered signal models (and SUSY mass ranges) and found to be negligible.
A second set of validation regions, not associated with any of the three signal regions, is used for general monitoring purposes. Two of the more significant backgrounds are dileptonic tt and lep-ton+hadronic τ tt events. To pass the four-jet requirement, such events must have at least one hard jet that does not originate from the tt decay (two hard jets for dileptonic tt). The modeling of these extra jets is validated in dedicated VRs that require either two signal leptons (electron or muon) or one signal lepton and one hadronic τ candidate. In Fig. 6 the jet multiplicity distributions are shown for event selections requiring an electron-muon pair (left) and one lepton plus one τ candidate (right). Additional validation regions are constructed by considering (1) events with high E miss T , high m T , and low am T2 for dilepton tt events with a lost lepton or (2)  of the resolution-induced m T tail in W+jets events (using the WVR-tail region in Fig. 2). There are no significant indications of mismodeling in any of the validation regions.

Systematic Uncertainties
The systematic uncertainties in the signal and background estimates arise both from experimental sources and from the uncertainties in the theoretical predictions and modeling. Since the yields from the dominant background sources, tt, single top, ttV, and W+jets, are all obtained in dedicated control regions, the modeling uncertainties for these processes affect only the extrapolation from the CRs into the signal regions (and between the various control regions), but not the overall normalization. The systematic uncertainties are included as nuisance parameters with Gaussian constraints and profiled in the likelihood fits. soft-term, i.e., from tracks neither associated with any reconstructed objects nor identified as originating from pileup. From these sources, the resulting uncertainties in the extrapolation factors for going from the four CRs to the SRs are 4-15% for JES, 0-9% for JER, 0-6% for b-tagging, and 0-3% for the E miss T soft-term. Other sources of experimental uncertainty are the modeling of lepton-and photon-related quantities (energy scales, resolutions, reconstruction and identification efficiencies, isolation, hadronic-τ identification) and the uncertainty in the integrated luminosity. These uncertainties have a small impact on the final results.
The uncertainties in the modeling of the single-top and tt backgrounds include effects related to the MC event generator, the hadronization and fragmentation modeling, and the amount of initial-and final-state radiation [71]. The MC generator uncertainty is estimated by comparing events produced with Powheg-Box+Herwig++ and with MG5_aMC+Herwig++. Events generated with Powheg-Box are hadronized with either Pythia or Herwig++ to estimate the effect from the modeling of the fragmentation and hadronization. The impact of altering the amount of initial-and final-state radiation is estimated from comparisons of Powheg-Box+Pythia samples with different parton shower radiation, NLO radiation, and modified factorization and renormalization scales. One additional uncertainty stems from the modeling of the interference between the tt and Wt processes at NLO. The uncertainty is estimated using inclusive WWbb events, generated using MG5_aMC, which are compared with the sum of the tt and Wt processes [71]. The resulting theoretical uncertainties in the extrapolation factors for going from the tt and Wt CRs to the SRs are 19-26% for tt, and 38-57% for Wt events, where the latter is dominated by the interference term.
The tt + Z background is normalized using the tt + γ CR and therefore there are uncertainties in both the kinematic extrapolation to the SR and in the conversion between the two processes. As described in Section 3, a small correction factor is applied to the tt + γ cross-section to account for differences in the generator setup, and the same K-factor is used for both processes. A first source of uncertainty is estimated by coherently varying the factorization and renormalization scales between tt + Z and tt + γ events generated at LO by a factor of two. The impact of the scale choice is slightly different between tt + Z and tt + γ, leading to a 10% uncertainty for high-p T bosons. An uncertainty due to NLO corrections is estimated by studying the kinematic dependence of the ratio of tt + Z and tt + γ K-factors. This ratio is studied by computing the K-factor for the tt + Z and tt + γ processes using MG5_aMC and OpenLoops+Sherpa as a function of the boson p T with a series of variations in the generator setup. Coherently varying the factorization and renormalization scale (set to H T = p T for both LO and NLO) by a factor of two results in a 5% uncertainty in the K-factor ratio. Comparing the results obtained with the NNPDF and the CT14 [127] PDF sets changes the K-factor ratio by less than 2%. A final uncertainty of 5% is due to the difference in K-factor ratios between the two generators when the same scale and PDF set is used, resulting from a different choice of electroweak scheme. The resulting theoretical systematic uncertainty in the extrapolation from the tt + γ CR to the SR is 12%.
The uncertainty in the W+jets background from the merging of matrix elements and parton showers is studied by varying the scales related to the matching scheme. In addition, the effects of varying the renormalization, factorization, and resummation scales are estimated. Since the W+jets background is normalized in a CR with a b-tagged jet veto, additional uncertainties in the flavor composition of the W+jets events in the signal region, based on the uncertainties in the measurement reported in Ref.
[128] extrapolated to higher jet multiplicities, are applied in all regions requiring at least one b-tagged jet. The resulting theoretical uncertainties in the extrapolation from the W+jets CR to the SR amount to about 40%.
Since the diboson backgrounds are not normalized in a CR, the analysis is sensitive to the uncertainty in the total cross-section, estimated to be 6%. In addition, the estimate from the nominal Sherpa sample is compared to that from a Powheg-Box+Pythia sample to account for differences related to the MC event generator modeling. The resulting theoretical uncertainties for the diboson yields in the three SRs are about 50%.
The SUSY signal cross-section uncertainty is taken from an envelope of cross-section predictions using different PDF sets and factorization and renormalization scales, as described in Ref. [129], and the resulting uncertainties range from 13% to 23%. The uncertainty in the VLQ signal cross-section is 10% [80].  Table 4. The uncertainty band includes statistical and all experimental systematic uncertainties. The last bin contains the overflow. Benchmark signal models are overlaid for comparison.

Results
Table 4 (top part) and Fig. 5 (right part) show the number of observed events together with the predicted number of background events in the three SRs. The prediction is obtained using the backgroundonly fit configuration described in Section 6. The SR2 and SR3 predicted yields agree well with the observed data in those regions. Table 4 (middle part) also lists the results for the four free fit parameters that control the normalization of the four main backgrounds (normalization factors, NFs), together with the associated fit uncertainties. To quantify the compatibility of the SM backgroundonly hypothesis with the observations in the SRs, a profile likelihood ratio test is performed. These fits are configured to include the SR bin in the likelihood. Table 4 reports the resulting p-values (p 0 ), which are set to 0.5 for SR2 and SR3 since the observation lies below the prediction. The data exceeds the background prediction in SR1 by 2.3 standard deviations. Four (eight) of the 12 observed events are in the electron (muon) channel. Figure 7 shows the E miss T and m T distributions in SR1 for the data, for the background prediction, as well as for two representative signal models.
The data are used to derive one-sided limits at 95% confidence level (CL) on generic beyond-SM yields and on the considered signal models. The results are obtained from a profile likelihood ratio test following the CL s prescription [130]. Model-independent upper limits on beyond-SM contributions are derived separately for each SR, where the fit is configured to include the SR and all its associated CRs. A generic signal model is assumed that contributes only to the SR and for which neither experimental nor theoretical systematic uncertainties except for the luminosity uncertainty are considered. The resulting limits, expected as well as observed, on the number of beyond-SM events are shown in the bottom rows of Table 4.
Exclusion limits are also derived for the gluino-mediated stop and direct stop pair production models. The signal uncertainties and potential signal contributions to all regions are taken into account. All uncertainties except those in 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 model. Figure 8 shows the expected and observed exclusion contours for both gluino-mediated and direct pair production of stops. The ±1 σ exp (yellow) uncertainty band indicates the impact on the expected limit of all uncertainties included in the fit. The ±1 σ th (dotted red) 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. The gap in the observed exclusion between about 600 and 750 GeV in the direct stop model is due to a transition between signal regions (SR1 has the best expected sensitivity up to around 750 GeV for a masslessχ 0 1 , beyond that SR2 has the best sensitivity) and the excess observed in SR1. The limits are sensitive to signal model assumptions. The gluino-mediated models have a 5 GeV mass splitting between the stop and the neutralino and a 100% branching ratio fort → c +χ 0 1 . The impact of varying both of these assumptions is studied for SR2 with a benchmark model characterized by masses for the gluino and the stop of (mg, mt 1 ) = (1250, 750) GeV. There is a small increase in the CL s value when increasing the mass gap from 5 to 20 GeV and from switching between the two-body stop decay and the four-body stop decayt → b f f χ 0 The search for direct gluino and direct stop production can also be used to set limits in other models of physics beyond the SM that produce tt + E miss T . Examples are third-generation leptoquarks [131-137], which decay into a top quark and a neutrino (LQ → tν), and VLQ (T ) models. For the former, limits on scalar LQ → tν are identical to limits on direct stop pair production with a massless neutralino and unpolarized top quarks. For the latter, simulated samples of pair-produced T quarks are used to reinterpret the results. The T quark is assumed to decay in three possible ways: T → tZ, T → tH, and T → bW. The search described in this paper has sensitivity mostly to the T → tZ decay mode with Z(→ νν) due to the large E miss T requirements in the analysis. The direct T pair production cross-section is higher than for stops due to additional spin states, but after accounting for the Z(→ νν) branching ratio, the models have a similar predicted yield. For a T quark with mass 800 GeV (just beyond the Run-1 limit [34, 138]), a branching ratio B (T → tZ) above about 90% is excluded. Figure 9 shows the exclusion limit as a function of the T quark mass. Assuming a branching ratio for T → tZ of 100%, T masses up to about 850 GeV are excluded.

Conclusion
This paper presents a search for pair production of gluino-mediated stops with a small mass splitting between the stop and the LSP, and direct pair production of stops decaying to two top quarks and two lightest neutralinos in final states with one isolated lepton, jets, and missing transverse momentum. Three signal region selections are optimized for discovery in benchmark models just beyond the exclusion limits from LHC Run-1 searches with the same tt + E miss T signature. The search uses        [119] C. G. Lester and B. Nachman, Bisection-based asymmetric M T 2 computation: a higher precision calculator than existing symmetric methods, JHEP 1503 (2015) 100, arXiv:1411.4312 [hep-ph].