Search for direct pair production of the top squark in all-hadronic final states in proton-proton collisions at $\sqrt{s}=8$ TeV with the ATLAS detector

The results of a search for direct pair production of the scalar partner to the top quark using an integrated luminosity of $20.1 \rm{fb}^{-1}$ of proton-proton collision data at $\sqrt{s}=8$ TeV recorded with the ATLAS detector at the LHC are reported. The top squark is assumed to decay via $\tilde{t} \rightarrow t \tilde{\chi}_{1}^{0}$ or $\tilde{t}\rightarrow b\tilde{\chi}_{1}^{\pm} \rightarrow b W^{\left(\ast\right)} \tilde{\chi}_{1}^{0}$, where $\tilde{\chi}_{1}^{0}$ ($\tilde{\chi}_{1}^{\pm}$) denotes the lightest neutralino (chargino) in supersymmetric models. The search targets a fully-hadronic final state in events with four or more jets and large missing transverse momentum. No significant excess over the Standard Model background prediction is observed, and exclusion limits are reported in terms of the top squark and neutralino masses and as a function of the branching fraction of $\tilde{t} \rightarrow t \tilde{\chi}_{1}^{0}$. For a branching fraction of 100%, top squark masses in the range 270-645 GeV are excluded for $\tilde{\chi}_{1}^{0}$ masses below 30 GeV. For a branching fraction of 50% to either $\tilde{t} \rightarrow t \tilde{\chi}_{1}^{0}$ or $\tilde{t}\rightarrow b\tilde{\chi}_{1}^{\pm}$, and assuming the $\tilde{\chi}_{1}^{\pm}$ mass to be twice the $\tilde{\chi}_{1}^{0}$ mass, top squark masses in the range 250-550 GeV are excluded for $\tilde{\chi}_{1}^{0}$ masses below 60 GeV.

In SUSY models, there are two scalar partners for the top quark (denotedt L andt R ), corresponding to left-handed and right-handed top quarks. Due to the large Yukawa coupling of the top quark, there can be significant mixing betweent L andt R , leading to a large splitting between the two mass eigenstates, denotedt 1 andt 2 , wheret 1 refers to the lighter of the two states. To leading order the direct top squark production cross section is given in perturbative Quantum Chromodynamics by gluon-gluon and qq fusion and depends only on thet 1 mass [28][29][30]. The decay of the top squark depends on the leftright admixture as well as on the masses and mixing parameters of the fermionic partners of the electroweak and Higgs bosons (collectively known as charginos,χ ± i , i = 1, 2 and neutralinos,χ 0 i , i = 1-4) to which the top squark can decay. No assumption is made on the LSP mass in this paper. While the LSP is assumed to be theχ 0 1 it could, for example, be a very light gravitino (the fermionic partner of the graviton), which would evade existing limits on the neutralino mass. In addition,t 1 is assumed to be heavier than the top quark and to decay via eithert 1 → tχ 0 1 ort 1 → bχ ± 1 → bW ( * )χ 0 1 , as illustrated in figure 1. This paper presents the results of a search for direct pair production oft 1 using a dataset corresponding to an integrated luminosity of L dt = 20.1 fb −1 . These data were collected by the ATLAS detector at the Large Hadron Collider (LHC) through proton- proton collisions at a centre-of-mass energy of √ s = 8 TeV. Only fully hadronic final states are considered. The undetected LSP,χ 0 1 , leads to missing transverse momentum (p miss T , whose magnitude is referred to as E miss T ). If both top squarks decay viat 1 → tχ 0 1 , the experimental signature is a pair of reconstructed hadronic top quarks plus significant E miss T . The bχ ± 1 → bW ( * )χ 0 1 decay mode leads to a similar final-state topology, apart from the mass of the resulting hadronic system. The results are presented as a function of the branching fraction B t 1 → tχ 0 1 . Previous searches for R-parity-conserving direct top squark production at centre-ofmass energies of 7 and 8 TeV have been reported by the ATLAS [31-37] and CMS [38][39][40][41][42][43] collaborations. The previous ATLAS search in the all-hadronic channel [32] considered only the nominal "fully resolved" experimental signature of six distinct jets (two from the bottom quarks and two from each of the W decays) and significant missing transverse momentum from the LSPs. In this paper, the experimental sensitivity to this signature is enhanced by considering in addition "partially resolved" events with four or five jets in the final state, which can occur if one or more jets are below the reconstruction threshold or if the decay products of Lorentz-boosted top quarks are sufficiently collimated. Furthermore, the sensitivity to thet 1 → bχ ± 1 decays is augmented by including events with exactly five jets in the final state (targeting final states where one of the jets from the W ( * ) decay has low transverse momentum, p T ).

The ATLAS detector
The ATLAS detector [44] consists of inner tracking devices surrounded by a superconducting solenoid, electromagnetic and hadronic calorimeters and a muon spectrometer in a toroidal magnetic field. The inner detector, in combination with the 2 T field from the solenoid, provides precise tracking of charged particles for |η| < 2.5. 1 It consists of a silicon pixel detector, a silicon strip detector and a straw-tube tracker that also provides transition radiation measurements for electron identification. A high-granularity electromagnetic calorimeter system, with acceptance covering |η| < 3.2, uses liquid argon (LAr) as the active medium. A scintillator-tile calorimeter provides hadronic coverage for |η| < 1.7. The end-cap and forward regions, spanning 1.5 < |η| < 4.9, are instrumented with LAr calorimeters for both electromagnetic and hadronic measurements. The muon spectrometer has separate trigger and high-precision tracking chambers which provide trigger coverage for |η| < 2.4 and muon identification and momentum measurements for |η| < 2.7.

Trigger and data collection
The data were collected from March to December 2012 at a pp centre-of-mass energy of 8 TeV using several triggers. For the primary search region, a missing transverse momentum trigger was used, which bases the bulk of its rejection on the vector sum of transverse energies deposited in projective trigger towers (each with a size of approximately ∆η × ∆φ ∼ 0.1 × 0.1 for |η| < 2.5; these are larger and less regular in the more forward regions). A more refined calculation based on the vector sum of all calorimeter cells above an energy threshold is made at a later stage in the trigger processing. The trigger required E miss T > 80 GeV, and is fully efficient for offline calibrated E miss T > 150 GeV in signal-like events. An integrated luminosity of L dt = (20.1 ± 0.6) fb −1 was collected using this trigger. The luminosity uncertainty is derived, following the same methodology as that detailed in ref.
[45], from a preliminary calibration of the luminosity scale obtained from beam-separation scans performed in November 2012.
Data samples enriched in the major sources of background were collected with electron or muon triggers, yielding an integrated luminosity of L dt = (20.3 ± 0.6) fb −1 . The electron trigger selects events based on the presence of clusters of energy in the electromagnetic calorimeter, with a shower shape consistent with that of an electron, a matching track in the tracking system, and a transverse energy (E T ) threshold of 24 GeV. In order to recover some of the efficiency for high-p T electrons, events were also collected with a single-electron trigger with looser requirements, but with the E T threshold set to 60 GeV. The muon trigger selects events containing one or more muon candidates based on tracks identified in the muon spectrometer and inner detector. For the single-muon trigger, the p T threshold was 24 GeV. To recover some of the efficiency for higher-p T muons, events were also collected with a single-muon trigger with a p T threshold of 36 GeV but with otherwise looser requirements.
Triggers based on the presence of high-p T jets were used to collect data samples for the estimation of the multijet and all-hadronic tt background. The jet p T thresholds ranged from 55 to 460 GeV. In order to stay within the bandwidth limits of the trigger system, only a fraction of events passing these triggers were recorded to permanent storage.

Simulated event samples and SUSY signal modelling
Samples of simulated events are used for the description of the background and to model the SUSY signal. Top quark pair production where at least one of the top quarks decays to a lepton is simulated with POWHEG-BOX [46]. To improve the agreement between data and simulation, tt events are reweighted based on the p T of the tt system; the weights are extracted from the ATLAS measurement of the tt differential cross section at 7 TeV, following the methods of ref.
[47] but updated to the full 7 TeV dataset. POWHEG-BOX is used to simulate single-top production in the s-and Wt-channels, while AcerMC [48] is used for the t-channel. SHERPA [49] is used for W + jets and Z + jets production with up to four additional partons (including heavy-flavour jets) as well as for diboson (WW , ZZ and W Z) production. MadGraph [50] generation with up to two additional partons is used for tt +W and tt + Z production.
The underlying-event model is the ATLAS AUET2B tune [51] of PYTHIA [52] except for the tt and single-top samples where the Perugia 2011 C tune [53] is used. The parton distribution function (PDF) sets used for the SM background are CT10 [54] for the POWHEG-BOX tt and SHERPA samples, and CTEQ6L1 [55] for the MadGraph, POWHEG-BOX single-top, and AcerMC samples.
For the initial comparison with data, all SM background cross sections are normalized to the results of higher-order calculations when available. The theoretical cross sections for W + jets and Z + jets are calculated with DYNNLO [56] with the MSTW 2008 NNLO [57] PDF set. The same ratio of the next-to-next-leading-order (NNLO) to leadingorder cross sections is applied to the production of W /Z in association with heavy-flavour jets. The inclusive tt cross section is calculated at NNLO, including resummation of next-to-next-to-leading-logarithmic (NNLL) soft gluon terms [58], with Top++ [59] using MSTW 2008 NNLO PDFs. The production cross sections of tt in association with W /Z are normalized to NLO cross sections [60,61]. Approximate NLO+NNLL calculations are used for single-top production cross sections [62][63][64]. For the diboson cross sections, MCFM [65] with MSTW 2008 NLO PDFs is used.
The signal samples are generated with three different configurations: (1) both top squarks decay viat 1 → tχ 0 1 , (2) one top squark decays viat 1 → tχ 0 1 and the other viat 1 → bχ ± 1 → bW ( * )χ 0 1 , and (3) both top squarks decay viat 1 → bχ ± 1 → bW ( * )χ 0 1 . With appropriate weighting of these configurations, the analysis sensitivity as a function of the branching fraction to tχ 0 1 can be assessed. In the samples with a decay to bχ ± 1 → bW ( * )χ 0 1 , the mass ofχ ± 1 is chosen to be twice that ofχ 0 1 (motivated by models of gaugino unification). The signal samples are generated in a grid across the plane of top squark andχ 0 1 masses with a grid spacing of 50 GeV across most of the plane. The top squark mass ranges from 200 to 750 GeV. In the samples for which both top squarks decay viat 1 → tχ 0 1 , theχ 0 1 mass ranges from 1 GeV up to approximately 5 GeV below the kinematic limit. For the samples involvingt 1 → bχ ± 1 → bW ( * )χ 0 1 decays, the chargino mass ranges from 100 GeV (taking into account the LEP limits [66] on the lightest chargino mass) up to approximately 10 GeV below thet 1 mass.
The signal samples for the scenario where both top squarks decay to a top quark and a neutralino are generated using Herwig++ [67]. The neutralino is fixed to be a pure bino, enhancing the decay of thet R component oft 1 to a right-handed top quark. Hadronic decays are expected to be less sensitive to such polarization effects; a subset of signal samples generated with top squarks corresponding to the left-handed top quark yielded a < 5% increase in the signal acceptance. The increase in the acceptance due to the polarization is neglected in this paper. The signal samples with mixed decays are generated using MadGraph. The differences between Herwig++ and MadGraph were evaluated for a few samples and found to be negligible. In these mixed decay samples, the chargino is fixed to be a pure wino, and thus top squark decays into bχ ± 1 originate from thet L component of the top squark. The signal samples for which both squarks decay to bχ ± 1 are generated with MadGraph where once again the chargino is fixed to be a pure wino. The PDF set used for all signal samples is CTEQ6L1.
All signal samples are normalized to cross sections calculated to NLO in the strong coupling constant, adding the resummation of soft gluon emission at next-to-leadinglogarithmic accuracy (NLO+ NLL) [28-30]. The nominal cross section and its uncertainty are taken from an envelope of cross-section predictions using different PDF sets and factorization and renormalization scales, as described in ref. [68]. The production cross section ranges from approximately 2 pb to 0.008 pb for a top squark mass of 300 GeV to 700 GeV respectively.
The detector simulation [69] is performed using GEANT4 [70] or a fast simulation framework where the showers in the electromagnetic and hadronic calorimeters are simulated with a parameterized description [71] and the rest of the detector is simulated with GEANT4. The fast simulation was validated against full GEANT4 simulation for several signal points. All samples are produced with a varying number of simulated minimumbias interactions overlaid on the hard-scattering event to account for multiple pp interactions in the same bunch crossing (pileup). The simulation is reweighted to match the distribution in data, which varies between approximately 10 and 30 interactions in each bunch crossing for this dataset. The overlay also treats the impact of pileup from bunch crossings other than the one in which the event occurred. Corrections are applied to the simulated samples to account for differences between data and simulation for the lepton trigger and reconstruction efficiencies, momentum scale and resolution, and for the efficiency of identifying jets originating from the fragmentation of b-quarks, together with the probability for mis-tagging light-flavour and charm quarks.

Physics object reconstruction
The reconstructed primary vertex [72] is required to be consistent with the luminous region and to have at least five associated tracks with p T > 400 MeV; when more than one such vertex is found, the vertex with the largest summed p 2 T of the associated tracks is chosen.
Jets are constructed from three-dimensional clusters of noise-suppressed calorimeter cells [73] using the anti-k t algorithm [74][75][76] with a distance parameter R = 0.4 and calibrated with a local cluster weighting algorithm [77]. An area-based correction is applied for energy from additional proton-proton collisions based on an estimate of the pileup activity in a given event using the method proposed in ref. [78]. Jets are calibrated [79] and required to have p T > 20 GeV and |η| < 4.5. Events containing jets arising from detector noise, cosmic-ray muons, or other non-collision sources are removed from consideration [79]. Once the E miss T is computed and any ambiguity with electrons or muons is resolved (as described below), signal jets are required to have p T > 35 GeV and |η| < 2.8. Jets containing a b-quark and within the acceptance of the inner detector (|η| < 2.5) are identified with an algorithm that exploits both the track impact parameters and secondary vertex information [80]; this algorithm is based on a neural network using the output weights of the IP3D, JetFitter+IP3D, and SV1 algorithms (defined in refs. [81,82]). The identification of these "b-tagged jets" has an average efficiency of 70% for jets originating from the fragmentation of a b-quark in simulated tt events, a rejection factor of approximately 150 for light-quark and gluon jets (depending on the p T of the jet), and a rejection factor of approximately 5 for charm jets.
Electrons, which are reconstructed from energy clusters in the electromagnetic calorimeter matched to a track in the inner detector [83], are required to have |η| < 2.47, p T > 10 GeV, and must pass a variant of the "loose" selection defined in ref. [83] that was reoptimized for 2012 data. In the case where the separation between an electron candidate and a non-b-tagged jet is ∆R < 0.2, the object is considered to be an electron. If the separation between an electron candidate and any jet satisfies 0.2 < ∆R < 0.4, or if the separation between an electron candidate and a b-tagged jet is ∆R < 0.2, the electron is not counted. Muons, which are 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 [84,85], are required to have |η| < 2.4 and p T > 10 GeV. If the separation between a muon and any jet is ∆R < 0.4, the muon is not counted.
The p miss T is the negative vector sum of the p T of the clusters of calorimeter cells, which are calibrated according to their associated reconstructed object (e.g. preselected jets and electrons), and the p T of preselected muons. The missing transverse momentum from the tracking system (denoted as p miss,track T , with magnitude E miss,track T ) is computed from the vector sum of the reconstructed inner detector tracks with p T > 500 MeV, |η| < 2.5, in association with the primary vertex in the event.
The requirements on electrons and muons are tightened for the selection of events in background control regions (described in section 7) containing leptons. Electrons are required to pass a variant of the "tight" selection of ref. [83] re-optimized for 2012 data, and are required to satisfy track-and calorimeter-based isolation criteria. The scalar sum of the p T of tracks within a cone of size ∆R = 0.3 ("track isolation") around the electron (excluding the electron itself) is required to be less than 16% of the electron p T . The scalar sum of the E T of pileup-corrected calorimeter energy deposits within a cone of size ∆R = 0.3 ("calorimeter isolation") around the electron (again, excluding the electron itself) is required to be less than 18% of the electron p T . The impact parameter of the electron in the transverse plane with respect to the reconstructed event primary vertex (|d 0 |) is required to be less than five times the impact parameter uncertainty (σ d0 ). The impact parameter along the beam direction, |z 0 × sin θ |, is required to be less than 0.4 mm. Further isolation criteria on reconstructed muons are also imposed: both the track and calorimeter isolation are required to be less than 12% of the muon p T . In addition, the requirements |d 0 | < 3σ d0 and |z 0 × sin θ | < 0.4 mm are imposed for muon candidates. The lepton p T requirements vary by background control region, as summarized in tables 5−7 in section 7.

Signal region definitions
The search for direct top squark pair production in the all-hadronic channel has a nominal experimental signature of six distinct jets (two of which originate from b-quarks), no reconstructed electrons or muons, and significant E miss T from the LSPs. The stringent requirement of E miss T > 150 GeV needed to satisfy the trigger rejects the vast majority of background from multijet and all-hadronic top quark events. Major background contributions include tt and W + jets events where one W decays via a low-momentum or misreconstructed lepton plus a neutrino; after the event selection described later in the text, approximately 40% of the tt background arises from a W decaying to a τ lepton that decays hadronically, while the remainder arises equally from W decays to an electron, muon or leptonically decaying τ. Other important background contributions are Z + jets and tt+Z events where the Z decays via neutrinos that escape detection, and single-top events.
This nominal signature, which is labelled "fully resolved" since all of the top squark decay products are individually reconstructed, is sensitive to a wide range of top squark and LSP masses in both thet → tχ 1 decay modes. The experimental sensitivity to thet → tχ 0 1 decay mode, especially for high top squark masses, is enhanced by also considering a second category of "partially resolved" events with particularly high E miss T and four or five reconstructed jets. This final state can occur if the top quarks are sufficiently Lorentz-boosted such that their decay products merge, and/or if one or more top decay products is below the reconstruction threshold. The consideration of a third category of events with exactly five jets in the final state but a less stringent E miss 1 and the other decays viat 1 → bχ ± 1 in each event, for mt 1 = 400 GeV, mχ± 1 = 200 GeV, and mχ0 1 = 100 GeV. Beyond these common requirements, the three categories of events are further subdivided and optimized individually to target the neutralino or chargino decay modes and particular top squark mass ranges. The most powerful discriminating variable is the E miss T resulting from the undetected LSPs; signal regions with higher (lower) E miss T requirements have increased sensitivity to potential signals where the difference in mass between the top squark and the LSP is large (small). The selection criteria obtained from the simulation-based optimization procedure are described in the following.

Fully resolved signal region (SRA)
This first category of events (SRA) encompasses the nominal signature of six jets plus E miss T . Events with additional jets from initial-or final-state radiation are also accepted. These events are then divided into four signal regions (SRA1-4) with increasing E miss T ; the specific requirements are summarized in table 2.
Since all jets from the top quark decays are fully resolved, the two top candidates are reconstructed from signal jets according to the following algorithm. The two jets with the highest b-tagging weight are selected first. From the remaining jets in the event, the two closest jets in the η-φ plane are combined to form a W boson candidate; this candidate is then combined with the b-tagged jet closest in the η-φ plane to form the first top candidate with mass m 0 b j j . A second W boson candidate is formed by repeating the procedure on the remaining jets; this candidate is then combined with the second of the selected b-tagged jets to form the second top candidate with mass m 1 b j j . The mass requirements on each top candidate are rather loose to ensure high signal efficiency.
Two additional discriminating quantities are introduced to reject the dominant tt background in these signal regions. The first quantity, min[m T jet i , p miss T ], is the minimum value of the transverse mass calculated from each of the signal jets and the p miss T , and ensures that the final-state jets are well separated from the p miss T . The second quantity is a "τ veto" in which events that contain a non-b-tagged jet within |η| < 2.5 with ≤ 4 associated tracks with p T > 500 MeV, and where the ∆φ between the jet and the p miss T is less than π/5 radians, are vetoed since they are likely to have originated from a W → τν decay.

Partially resolved signal region targetingt
An alternative top reconstruction algorithm is applied to events with four or five jets in the final state (SRB). The anti-k t clustering algorithm [74] is applied to R = 0.4 signal jets, using reclustered distance parameters of R = 0.8 and R = 1.2. Nominally, the all-hadronic decay products of a top quark can be reconstructed as three distinct jets, each with a distance parameter of R = 0.4. The transverse shape of these jets are typically circular with a radius equal to this distance parameter, but when two of the jets are less than 2R apart in ηφ space, the one-to-one correspondence of a jet with a top daughter is violated. To some extent, this can be tolerated in the fully resolved scenario without an appreciable efficiency loss, but as the jets become closer together the majority of the p T is attributed to one of the two jets, and the lower-p T jet may drop below the minimum p T requirement. In SRB, at least two reclustered R = 1.2 jets are required, and selection criteria are employed based on the masses of these top candidates: m 0 jet, R=1.2 m 1 jet, R=1.2 is the mass of the highest-p T (second-highest-p T ) anti-k t R = 1.2 reclustered jet. Requirements are also placed on the p T of the highest-p T anti-k t R = 1.2 reclustered jet (p 0 T,jet, R=1.2 ) and the mass of the highest-p T anti-k t R = 0.8 reclustered jet (m 0 jet, R=0.8 ); this latter requirement rejects background without hadronic W candidates.
For signal regions employing reclustered jets, it is useful to categorize events based on the top mass asymmetry A m t , defined as: Events where A m t < 0.5 tend to be well balanced, with two well reconstructed top candidates (SRB1). In events where A m t > 0.5 the top candidates tend to be overlapping or otherwise less well reconstructed (SRB2). Since the two categories of events have markedly different signal-to-background ratios, the selections for these two categories of events are optimized separately.
The background in SRB, which is dominated by Z + jets and W + jets, is suppressed by requirements on the transverse mass of the p miss T and the non-b-tagged jet closest in ∆φ to the p miss T , m min T , and the transverse mass of the fourth jet (in p T order) and the p miss T , m T jet 3 , p miss T ; this latter variable is used only in four-jet events in SRB1. In SRB2, where the top candidates tend to be less well-reconstructed and background rejection is especially challenging, only five-jet events are considered and an additional requirement is made on a measure of the E miss where H T is the scalar sum of the p T of all five jets in the event. The full set of selection requirements for SRB are detailed in table 3; the logical OR of SRB1 and SRB2 is considered in the final likelihood fit.  Table 2. Selection criteria for SRA, the fully resolved topology, with ≥ 6 anti-k t R = 0.4 jets. Table 3. Selection criteria for SRB, the partially resolved topology, with four or five anti-k t R = 0.4 jets, reclustered into anti-k t R = 1.2 and R = 0.8 jets.  Table 4. Selection criteria for SRC, targeting the scenario in which one top squark decays viã at the expense of increased background. Additional discrimination against background where the two b-tagged jets come from a gluon emission is provided by a requirement on |∆φ (b, b)|, the azimuthal angle between the two highest-p T b-tagged jets. To reduce the tt background, tighter requirements on m b, min T are employed. The quantity m b, max T is also used, which is analogous to m b, min T except that the transverse mass is computed with the b-tagged jet that has the largest ∆φ with respect to the p miss T direction. These two criteria, along with the E miss T , are tightened in subsequent SRC1-3 sub-regions as summarized in table 4. Finally, the same τ veto as described in section 6.1 is applied.

Background estimation
The main background contributions in SRA and SRC arise from tt production where one top quark decays semileptonically and the lepton (particularly a hadronically decaying τ lepton) is either not identified or reconstructed as a jet, Z(→ νν) plus heavy-flavour jets, and the irreducible background from tt+Z(→ νν). In SRB, an important contribution comes from W plus heavy-flavour jets, where again the W decays semileptonically and the lepton is reconstructed as a jet or not identified. Other background processes considered are multijets, single top, tt +W , and diboson production.
With the exception of all-hadronic tt and multijet production, all background contributions are estimated primarily from simulation. Control regions (CRs) are used to adjust the normalization of the simulated background contributions in each signal region from semileptonic tt, Z → νν plus heavy-flavour jets and, in the case of SRB, W plus heavyflavour jets. The all-hadronic tt and multijet contributions are estimated from data alone in a multijet control region. The control regions are designed to be orthogonal to the signal regions while enhancing a particular source of background; they are used to normalize the simulation for that background to data. The control regions are chosen to be kinematically close to the corresponding signal region, to minimize the systematic uncertainty associated with extrapolating the background yield from the control region to the signal region, but also to have enough data events to avoid a large statistical uncertainty in the background estimate. In addition, control region selections are chosen to minimize potential contamination from signal in the scenarios considered. As the control regions are not always pure in the process of interest, simulation is used to estimate the cross contamination between control regions; the normalization factors and the cross contamination are determined simultaneously for all regions using a fit described in section 7.5.
The selection requirements for all control regions used in this analysis are summarized in tables 5, 6, and 7 for SRA, SRB, and SRC, respectively.

tt background
The control region for the semileptonic tt background is defined with requirements similar to those described in section 6 for the top squark signal candidates; however, in order to enhance the contribution from the semileptonic tt process, the events are required to be based on the single-electron or single-muon trigger and to contain a single isolated electron or muon as described in section 5. The transverse mass of the lepton and E miss T is required to be close to the W mass, namely between 40 and 120 GeV. Events with an additional isolated electron or muon with transverse momentum greater than 10 GeV are rejected. The identified lepton is then treated as a non-b-tagged jet before imposing the jet and b-tagged jet multiplicity requirements. Several signal region requirements are relaxed (or not applied at all) in order to have enough events, while keeping systematic uncertainties related to extrapolating the background yield from the control region to the signal region under control. Figure 3 compares several distributions in data and simulation in the semileptonic tt control region for each signal region; the background expectations are normalized using the factors summarized in table 8.

W + jets background
For SRB only, a control region is defined for the normalization of the W + jets background. The control region requirements are similar to those in the tt control region for SRB but a number of requirements are changed in order to enhance the W plus heavy-flavour jets process over tt. The top mass asymmetry in eq. 6.2 is restricted to the region A m t < 0.5, the number of b-tagged jets is required to be exactly one, and the mass of the leading anti-k t R = 1.2 reclustered jet is required to be less than 40 GeV. The full list of requirements can be found in table 6. The lepton is treated as a non-b-tagged jet (in a similar fashion as the tt control region) before imposing the jet and b-tagged jet multiplicity requirements. Table 6. Selection criteria for control regions associated with SRB. Only the requirements that differ from the common selection in table 1 and those in table 3 are listed; "same" indicates the same selection as the signal region.

Z + jets background
The control region for Z(→ νν) plus heavy-flavour jets background is based on a sample of Z(→ )+jets events (where denotes either an electron or muon). The events are collected with the single-lepton triggers. Exactly two oppositely charged electrons or muons are required; the higher-p T lepton must satisfy p T > 25 GeV and the lower-p T lepton must satisfy p 2 T > 10 GeV. The invariant mass of the dilepton pair (m ) is required to be between 86 and 96 GeV. To reduce the tt contamination, the events are required to have E miss T < 50 GeV. The reconstructed dileptons are then removed from the event to mimic the Z(→ νν) decay and the vector sum of their momenta is added to the p miss T ; the events are required to have a recalculated E miss T > 70 GeV. No requirements are made on the number of b-tagged jets. Monte Carlo studies indicate that the E miss T in Z+jets events (with Z(→ νν)) is completely dominated by the neutrinos from the Z decay, independent of the presence of b-tagged jets. The shape of the E miss T distribution, comparing data to simulation, is shown in figure 5(a); the normalization of the simulation for the estimation of the background is described below.
The fraction of events containing two or more b-tagged jets (henceforth denoted the bb-fraction) is found in simulation and data to scale linearly with the number of jets in the event as shown in figure 5(b), as expected when the primary source of b-tagged jet pairs is gluon radiation followed by splitting. The number of events in the Z + jets control region is corrected in each jet multiplicity bin in simulation and data by the bb-fraction. The bbfraction is fit to a linear function of jet multiplicity, starting at a jet multiplicity of two, in order to improve the statistical accuracy for high jet-multiplicity Z events. After correcting for the bb-fraction, the Z + jets simulation is normalized to the data in the control region.

Multijet background
The multijet (including fully hadronic tt) background is evaluated using the jet-smearing technique described in ref. [86]. The basic concept is to take a sample of well-measured multijet events in the data (based on low values of E miss T / √ ΣE T , where ΣE T is the scalar sum of the transverse energy in the event recorded in the calorimeter systems) and to smear the jet momentum and φ direction with jet response functions, determined with PYTHIA8 [87] and corrected with data, separately for light-flavour and heavy-flavour jets. This sample of smeared events is normalized to the data in a control region enriched in multijet events. The same jet multiplicity requirements are applied as in the signal regions, including the requirement of two or more b-tagged jets. The calorimeter-based (trackbased) E miss T is required to be greater than 150 (30) GeV. The signal region requirement on the azimuthal separation ∆φ jet, p miss T is inverted to enhance the population of mismeasured multijet events. Figure 6   1.07 ± 0.07 1.07 ± 0.07

Simultaneous fit to determine SM background
The observed numbers of events in the various control regions are included in a profile likelihood fit to determine the SM background estimates in each signal region. This procedure takes common systematic uncertainties (discussed in detail in section 8) between the control and signal regions and their correlations into account; they are treated as nuisance parameters in the fit and are modelled by Gaussian probability density functions. For SRA and SRC, the free parameters in the fit are the overall normalizations of the tt, Z + jets, and multijet background. 2 For SRB the normalization of the W + jets background is also a free parameter. The contributions from all other background processes are fixed at the values expected from the simulation, using the most accurate theoretical cross sections available, as described in section 4. The fit to the control regions yields normalization factors for each background source; these are summarized in table 8. The resulting yields in the control regions (before and after the fit) are summarized in table 9. The contamination due to potential signal events in the control regions is negligible (at most a few per cent). The background estimates are validated by predicting the background in dedicated regions and comparing to observation. The validation regions are designed to be orthogonal to the control and signal regions while retaining kinematics and event composition close to the SRs but with little contribution from signal in any of the models considered. For SRA, two validation regions are defined. In the first region (VRA1), all of the requirements for SRA1 are applied except for those on the top mass, and the τ veto is inverted. In the second region (VRA2), all of the SRA1 requirements are applied except for those on the top mass, and m b, min T is required to be between 125 and 175 GeV. For SRB, the validation region (VRB) is formed from the logical OR of SRB1 and SRB2 except that the E miss T requirement is loosened to E miss T > 150 GeV, m b, min T is required to be between 100 and 175 GeV, and none of the other transverse mass requirements are applied. For SRC, the validation regions consist of all the SRC1 requirements except that m b, min T is required to be between 150 and 185 GeV and m b, max T is required to be greater than 125 GeV, and the τ veto is either inverted (VRC1) or applied (VRC2). All five validation regions are dominated by tt background. The background yield in each validation region, predicted from the fit to the control regions, is consistent with the observed number of events to within one standard deviation; these results are summarized in table 10.

Systematic uncertainties
Systematic uncertainties in the SM background estimates and signal expectations are evaluated and included in the profile likelihood fit described in section 7.5. The impact of each source of systematic uncertainty is quantified as a percentage of the total background estimate (signal expectation) after propagating the uncertainty from the relevant nuisance parameter, keeping all other fit parameters fixed. All correlations with the other parameters of interest are taken into account.
The main sources of detector-related systematic uncertainties in the SM background estimates are the jet energy resolution (JER) and jet energy scale (JES). These jet reconstruction uncertainties are propagated to all quantities that depend on the jet energies such as the reconstructed top mass and the E miss T . Additional uncertainties in E miss T that arise from energy deposits unassociated with reconstructed objects are also included. The impact of these uncertainties is mitigated by the normalization of the dominant SM background contributions in the kinematically similar control regions. The JER uncertainty is derived from in-situ measurements of the jet response asymmetry in dijet events [79]; the effect of this uncertainty on the background estimates in the signal regions ranges from 6-15% in SRA, 16% in SRB, and 3-6% in SRC. The JES uncertainty is determined using the techniques described in refs. [79,88]; the uncertainties are determined in bins of jet η and p T and depend on jet flavour and the number of primary vertices in an event. The effect of the JES uncertainty on the background estimate ranges from 5-9% in SRA, 6% in SRB, and 8-11% in SRC. Other uncertainties arising from the simulation of b-tagging, pileup, the τ veto, and E miss,track T are negligible by comparison. A 2.8% uncertainty in the luminosity determination [45] is included for all signal and background MC simulations.
Theoretical uncertainties in the modelling of the SM background are evaluated; their impact is mitigated by the use of control regions to normalize the background contributions. For the tt background, uncertainties due to the choice of parton shower (PYTHIA vs. HERWIG [89]+JIMMY [90]), the renormalization and factorization scales (each varied up and down by a factor of two), the amount of initial-and final-state radiation (using AcerMC samples with differing parton shower settings, constrained by measurement [91]), and the PDF uncertainties (derived from the envelope of variations of the CT10 PDF summed in quadrature with the difference with respect to the HERA PDFs [92]) are evaluated. The resulting uncertainties in the total background yields are less than 10% in SRA and SRC (the signal regions with an appreciable contribution from tt production). For tt +W /Z background, the theoretical uncertainty is dominated by the 22% uncertainty [60, 93] on the NLO cross section. Additional variations considered include the choice of renormalization and factorization scales (each varied up and down by a factor of two), the amount of initial-and final-state radiation (using simulated MadGraph samples), and the matching scale at which additional jets from the matrix element are distinguished from those generated by the parton shower. Finally the uncertainty arising from the use of a finite number of additional partons in the matrix element is assessed by comparing event yields from samples with one versus two additional partons in the matrix element. The resulting impact on the total background yields range from 3-6% in SRA, 6% in SRB, and is at the per cent level in SRC.
Systematic uncertainties in the modelling of the W + jets background are evaluated with respect to the choice of renormalization and factorization scales (each varied up and down by a factor of two), the matching scale, the PDF uncertainties, and event generation with a finite number of partons (comparing samples with four versus five additional partons in the matrix element). An uncertainty of 38% is applied to the W + heavy flavour production cross section; this is derived from the measurement in ref.
[94] and extrapolated to events with at least five jets. An additional uncertainty of 20% is applied to the W + jets control region for SRB to account for differing fractions of W + c vs. W + bb/cc in the control region compared to the signal region. For the Z + jets background, the uncertainties due to the choice of generator (ALPGEN vs. SHERPA), the PDF uncertainties, and event generation with a finite number of partons are evaluated. The resulting impact on the total background yields from all of the above-mentioned W + jets (Z + jets) theoretical uncertainties are 1-2% (1-2%) in SRA, 10% (9%) in SRB, and 5% (4-5%) in SRC. An additional systematic uncertainty of 17% is assigned to the background yield from the uncertainty in the linear fit to the bb-fraction in the Z + jets control region described in section 7.3.
The single-top background is dominated by the Wt subprocess; the cross-section uncertainty is taken from ref. [63]. Additional uncertainties are evaluated for the selection of generator (MC@NLO vs. POWHEG-BOX), parton shower, initial-and final-state radiation, and PDF choices. Finally, the effect of the interference between single-top and tt production is evaluated from a comparison of the sum of tt and single-top background from POWHEG-BOX with the background from an AcerMC sample of the inclusive W bW b final state. The resulting uncertainty in the total background estimate ranges between 1% and 5%, depending on the signal region. An uncertainty of 50% is assigned to diboson production, resulting in uncertainties in the total background yield of < 1% in all signal regions. An uncertainty of 100% is assigned to the small multijet background, with negligible impact on the total background uncertainty.
The theoretical uncertainties in the top squark production cross section include uncertainties due to the chosen PDF, factorization and renormalization scales, and strong coupling constant variations. These uncertainties are not included as nuisance parameters in the fit; instead, their impact is shown explicitly in the results. In contrast, systematic uncertainties in the signal acceptance are included as nuisance parameters in the fit. The impact on the signal acceptance of variations in the PDF, factorization and renormalization scales, and strong coupling constant is found to be negligible. The systematic uncertainty in the signal acceptance due to the modelling of initial-state radiation is negligible in the region where this analysis has sensitivity to top squark production. Detector-related systematic uncertainties in the signal acceptance are dominated by the JES (4-16% effect on the signal yield in SRA, 3% in SRB, 4-10% in SRC), b-tagging (7-8% in all signal regions) uncertainties and JER (2-10% in SRA, 10% in SRB and 2-3% in SRC). All detector-related uncertainties are assumed to be fully correlated with those of the background.

Results and interpretation
The numbers of events observed in data in each of the eight signal regions are presented in table 11. These results are compared to the total number of expected background events in each signal region. The total background estimate is determined from the simultaneous fit based on the profile likelihood method [95] using a procedure similar to that described in section 7.5 but including the corresponding signal regions as well as control regions. The E miss T distributions for each signal region are displayed in figure 7; the distributions for SRA1 and SRA2 as well as SRA3 and SRA4 are combined since they only differ by the E miss T requirement. In these figures, the background expectations are normalized by the factors given in table 8.
No significant excess above the SM expectation is observed in any of the signal regions. The probabilities are all consistent with the background-only hypothesis; the smallest p 0 value is 0.19 for SRA4. The 95% confidence level (CL) upper limits on the number of beyond-the-SM (BSM) events in each signal region are derived using the CL s prescription [96] and calculated from asymptotic formulae [95]. Any possible signal contamination in the control regions is neglected. The BSM signal strength is included as a free parameter but constrained to be non-negative. Normalizing the upper limits on the numbers of events by the integrated luminosity of the data sample, they can be interpreted as model-independent limits on the visible BSM cross sections, defined as σ vis = σ · A · ε, where σ is the production cross section, A is the acceptance, and ε is the selection efficiency for a BSM signal. Table 11 summarizes these upper limits for each signal region. A comparison between results obtained using pseudo-experiments and the asymptotic approximation was performed; the two methods are found to be in good agreement.
The results from the simultaneous fit to the signal and control regions are used to set limits on direct top squark pair production except that a fixed signal component is used here and any signal contamination in the CRs is taken into account. Again, limits are derived using the CL s prescription and calculated from asymptotic formulae. By design, SRA is orthogonal to SRB and SRC. However, SRB and SRC are not independent (each considers five-jet events). Therefore each of SRA1-4 is statistically combined both with SRB (SRA+SRB) and with each of SRC1-3 (SRA+SRC). The SRA+SRB or SRA+SRC combination with the smallest expected 95% CL s value is chosen for eacht 1 andχ 0 1 mass. In these combinations, the signal and detector-related systematic uncertainties are treated as correlated while the theoretical uncertainties and those due to the background normalizations in the independent control regions are treated as uncorrelated. 'Expected' limits are calculated by setting the nominal event yield in each SR to the mean background expectation; contours that correspond to ±1σ uncertainties in the background estimates (σ exp ) are also evaluated. 'Observed' limits for each channel are calculated from the observed event yields in the signal regions for the nominal signal cross sections and ±1σ theory uncertainties (σ SUSY theory ). Numbers quoted in the text are evaluated from the observed exclusion limit based on the nominal cross section minus 1σ SUSY theory .    values: 100%, 75%, 50%, 25%, and 0%, where 0% indicates that both top squarks decay exclusively viã t → bχ   The excluded mass ranges correspond to the observed limit minus one standard deviation of the uncertainty in the signal cross section (the inner red dotted contour in figure 8, for example)

Conclusions
The results of a search for direct top squark production with an all-hadronic experimental signature of jets and missing transverse momentum are presented, using an integrated luminosity of 20.1 fb −1 of proton-proton collision data at √ s = 8 TeV collected by the AT-LAS detector at the LHC. In this search, the top squark is assumed to decay viat → tχ 0 1 or t → bχ ± 1 . In addition to the nominal fully resolved topology that requires at least six jets, the sensitivity of the analysis is increased by including a partially resolved topology (four or five jets). Furthermore, a dedicated signal region requiring exactly five jets augments the sensitivity to top squark decays viat → bχ [36] ATLAS Collaboration, Search for direct third-generation squark pair production in final states with missing transverse momentum and two b-jets in √ s = 8 TeV pp collisions with the ATLAS detector, JHEP 10 (2013) 189, [arXiv:1308.2631].
[37] ATLAS Collaboration, Search for direct top squark pair production in events with a Z boson, b-jets and missing transverse momentum in √ s=8 TeV pp collisions with the ATLAS detector, arXiv:1403.5222.
[40] CMS Collaboration, Search for supersymmetry in hadronic final states with missing transverse energy using the variables α T and b-quark multiplicity in pp collisions at 8