A search for top squarks with R-parity-violating decays to all-hadronic final states with the ATLAS detector in $\sqrt{s}$ = 8 TeV proton-proton collisions

A search for the pair production of top squarks, each with R-parity-violating decays into two Standard Model quarks, is performed using 17.4 fb$^{-1}$ of $\sqrt{s}$ = 8 TeV proton-proton collision data recorded by the ATLAS experiment at the LHC. Each top squark is assumed to decay to a b- and an s-quark, leading to four quarks in the final state. Background discrimination is achieved with the use of b-tagging and selections on the mass and substructure of large-radius jets, providing sensitivity to top squark masses as low as 100 GeV. No evidence of an excess beyond the Standard Model background prediction is observed and top squarks decaying to $\bar{b}\bar{s}$ are excluded for top squark masses in the range $100 \leq m_{\tilde{t}} \leq 315$ GeV at 95% confidence level.


Introduction
Supersymmetry (SUSY) is an extension of the Standard Model (SM) [1][2][3][4][5][6][7] that fundamentally relates fermions and bosons. It is an especially alluring theoretical possibility given its potential to solve the hierarchy problem [8][9][10][11] and to provide a dark-matter candidate [12,13]. This paper presents a search for the pair production of supersymmetric top squarks (stops) 1 , which then each decay to two SM quarks, using 17.4 fb −1 of √ s = 8 TeV proton-proton (pp) collision data recorded by the ATLAS experiment at the Large Hadron Collider (LHC). This decay violates the R-parity conservation (RPC) [14] assumed by most searches for stops [15,16]. In RPC scenarios, SUSY particles are required to be produced in pairs and decay to the lightest supersymmetric particle (LSP), which is stable. In R-parity-violating (RPV) models, decays to only SM particles are allowed, and generally relax the strong constraints now placed on standard RPC SUSY scenarios by the LHC experiments. It is therefore crucial to expand the scope of the SUSY search programme to include RPV models. Common signatures used for RPV searches include resonant lepton-pair production [17], exotic decays of long-lived particles with displaced vertices [18][19][20][21], high lepton multiplicities [22,23], and high-jet-multiplicity final states [24]. Scenarios which have stops of mass below 1 TeV are of particular interest as these address the hierarchy problem [25][26][27][28].
SUSY RPV decays to SM quarks and leptons are controlled by three Yukawa couplings in the generic supersymmetric superpotential [29,30]. These couplings are represented by λ i jk , λ i jk , λ i jk , where i, j, k ∈ 1, 2, 3 are generation indices that are sometimes omitted in the discussion that follows. The first two (λ, λ ) are lepton-number-violating couplings, whereas the third (λ ) violates baryon number. It is therefore generally necessary that either of the couplings to quarks, λ or λ , be vanishingly small to prevent spontaneous proton decay [7]. It is common to consider non-zero values of each coupling separately. Scenarios in which λ 0 are often referred to UDD scenarios because of the baryon-number-violating term that λ controls in the superpotential. Current indirect experimental constraints [31] on the sizes of each of the UDD couplings λ from sources other than proton decay are primarily valid for low squark mass and for first-and second-generation couplings. Those limits are driven by double nucleon decay [32] (for λ 112 ), neutron oscillations [33] (for λ 113 ), and Z-boson branching ratios [34].
The benchmark model considered in this paper is a baryon-number-violating RPV scenario in which the stop is the LSP. The search specifically targets low-mass stops in the range 100-400 GeV that decay via the λ 323 coupling, thus resulting in stop decayst →bs (assuming a 100% branching ratio) as shown in Figure 1. The motivation to focus on the third-generation UDD coupling originates primarily from the minimal flavour violation (MFV) hypothesis [35] and the potential for this decay channel to yield a possible signal of RPV SUSY with a viable dark-matter candidate [36]. The MFV hypothesis essentially requires that all flavour-and CP-violating interactions are linked to the known structure of Yukawa couplings, and has been used to argue for the importance of the λ couplings [37].
The processtt * →bsbs represents an important channel in which to search for SUSY in scenarios not yet excluded by LHC data [36][37][38]. Some of the best constraints on this process are from the ALEPH Collaboration, which set lower bounds on the mass of the stop at mt 80 GeV [39]. The CDF Collaboration extended these limits, excluding 50 mt 90 GeV [40]. The CMS Collaboration recently released the results of a search that excludes 200 mt 385 GeV [41] in the case where heavy-flavour jets are present in the final state. In addition, two ATLAS searches have placed constraints on RPV stops that decay tobs when they are produced in the decays of light gluinos (mg 900-1000 GeV) [42,43]. The search presented here specifically focuses on direct stop pair production and seeks to close the gap in excluded stop mass between ∼ 100-200 GeV. Contributions from RPV interactions at production -such as would be required for resonant single stop production -are neglected in this analysis. This approach is valid provided that the RPV interaction strength is small compared to the strong coupling constant, which is the case for λ 323 10 −2 -10 −1 [44] and for the estimated size of λ 323 ∼ 10 −4 from MFV in the model described in Ref. [37].
The reduced sensitivity of standard SUSY searches to RPV scenarios is primarily due to the limited effectiveness of the high missing transverse momentum requirements used in the event selection common to many of those searches, motivated by the assumed presence of undetected LSPs. Consequently, the primary challenge in searches for RPV SUSY final states is to identify suitable substitutes for background rejection to the canonical large missing transverse momentum signature. Backgrounds dominated by multijet final states typically overwhelm the signal in the four-jet topology. In order to overcome this challenge, new observables are employed to search fortt * →bsbs in the lowmt regime [38]. For mt ≈ 100-300 GeV, the initial stop transverse momentum (p T ) spectrum extends significantly into the range for which p T mt. This feature is the result of boosts received from initialstate radiation (ISR) as well as originating from the parton distribution functions (PDFs). As the Lorentz boost of each stop becomes large, the stop decay products begin to merge with a radius roughly given by ∆R ≈ 2mt/p T , and thus can be clustered together within a single large-radius (large-R) jet with a mass m jet ≈ mt. By focusing on such cases, the dijet and multijet background can be significantly reduced via selections that exploit this kinematic relationship and the structure of the resulting stop jet, in a similar way to boosted objects used in previous measurements and searches by ATLAS [45][46][47][48][49]. In this case, since the stop is directly produced in pairs instead of from the decay of a massive parent particle, the strategy is most effective at low mt where the boosts are the largest.
The ID comprises a silicon pixel tracker closest to the beamline, a microstrip silicon tracker, and a strawtube transition-radiation tracker at radii up to 108 cm. A thin solenoid surrounding the tracker provides a 2 T axial magnetic field enabling the measurement of charged-particle momenta. The overall ID acceptance spans the full azimuthal range in φ, and the range |η| < 2.5 for particles originating near the nominal LHC interaction region [52].
A three-level trigger system is used to select events to record for offline analysis. The different parts of the trigger system are referred to as the level-1 trigger, the level-2 trigger, and the event filter [53]. The level-1 trigger is implemented in hardware and uses a subset of detector information to reduce the event rate to a design value of at most 75 kHz. The level-1 trigger is followed by two software-based triggers, the level-2 trigger and the event filter, which together reduce the event rate to a few hundred Hz. The search presented in this document uses a trigger that requires a high-p T jet and a large summed jet transverse momentum (H T ), as described in Section 5.

Monte Carlo simulation samples
Monte Carlo (MC) simulation is used to study the signal acceptance and systematic uncertainties, to test the background estimation methods used, and to estimate the tt background. In all cases, events are passed through the full GEANT4 [54] detector simulation of ATLAS [55] after the simulation of the parton shower and hadronisation processes. Following the detector simulation, identical event reconstruction and selection criteria are applied to both the MC simulation and to the data. Multiple pp collisions in the same and neighbouring bunch crossings (pile-up) are simulated for all samples by overlaying additional soft pp collisions which are generated with PYTHIA 8.160 [56] using the ATLAS A2 set of tuned parameters (tune) in the MC generator [57] and the MSTW2008LO PDF set [58]. These additional interactions are overlaid onto the hard scatter and events are reweighted such that the MC distribution of the average number of pp interactions per bunch crossing matches the measured distribution in the full 8 TeV data sample. 2 The ATLAS reference system is a Cartesian right-handed coordinate system, with the nominal collision point at the origin.
The anticlockwise beam direction defines the positive z-axis, while the positive x-axis is defined as pointing from the collision point to the centre of the LHC ring and the positive y-axis points upwards. The azimuthal angle φ is measured around the beam axis, and the polar angle θ is measured with respect to the z-axis. Pseudorapidity is defined as η = − ln[tan(θ/2)], rapidity is defined as y = 0.5 ln[(E + p z )/(E − p z )], where E is the energy and p z is the z-component of the momentum, and transverse energy is defined as E T = E sin θ.
The signal process is simulated using Herwig++ 2.6.3a [59] with the UEEE3 tune [60] for several stopmass hypotheses using the PDF set CTEQ6L1 [61,62]. All non-SM particles masses are set to 5 TeV except for the stop mass, which is scanned in 25 GeV steps from mt = 100 GeV to mt = 400 GeV.
The signal cross-section used (shown in Figure 2) is calculated to next-to-leading order in the strong coupling constant, adding the resummation of soft gluon emission at next-to-leading-logarithmic accuracy (NLO+NLL) [63][64][65]. For the range of stop masses considered, the uncertainty on the cross-section is approximately 15% [66]. MadGraph 5.1.4.8 [67] is used to study the impact of ISR on the stop p T spectrum. The MadGraph samples have one additional parton in the matrix element, which improves the modelling of a hard ISR jet. MadGraph is then interfaced to PYTHIA 6.426 with the AUET2B tune [68] and the CTEQ6L1 PDF set for parton shower and hadronisation. The distribution of p T (tt * ) from the nominal Herwig++ signal sample is then reweighted to match that of the MadGraph+PYTHIA sample.
Dijet and multijet events, as well as top quark pair (tt) production processes, are simulated in order to study the SM contributions and background estimation techniques. For optimisation studies, SM dijet and multijet events are generated using Herwig++ 2.6.3a with the CTEQ6L1 PDF set. Top quark pair events are generated with the POWHEG-BOX-r2129 [69][70][71] event generator with the CT10 NLO PDF set [72]. These events are then interfaced to PYTHIA 6.426 with the P2011C tune [73] and the same CTEQ6L1 PDF set as Herwig++.
The value of the tt cross-section is σ tt = 253 +13 −15 pb.

Object definitions
The data are required to have satisfied criteria designed to reject events with significant contamination from detector noise, non-collision beam backgrounds, cosmic rays, and other spurious effects. To reject non-collision beam backgrounds and cosmic rays, events are required to contain a primary vertex consistent with the LHC beamspot, reconstructed from at least two tracks with transverse momenta p track T > 400 MeV. If more than one vertex satisfies these criteria, the primary vertex is chosen as the one with the highest tracks (p 2 T ). The anti-k t algorithm [80], with a radius parameter of R = 0.4, is used for initial jet-finding using version 3 of FastJet [81]. The inputs to the jet reconstruction are three-dimensional topo-clusters [82]. This method first clusters together topologically connected calorimeter cells and classifies these clusters as either electromagnetic or hadronic. The classification uses a local cluster weighting calibration scheme based on cell-energy density and shower depth within the calorimeter [83]. Based on this classification, energy corrections are applied which are derived from single-pion MC simulations. Dedicated hadronic corrections are derived to account for the effects of differences in response to hadrons compared to electrons, signal losses due to noise-suppression threshold effects, and energy lost in non-instrumented regions. The final jet energy calibration is derived from MC simulation as a correction relating the calorimeter response to the jet energy at generator level. In order to determine these corrections, the same jet definition used in the reconstruction is applied to stable (with lifetimes greater than 10 ps) generator-level particles, excluding muons and neutrinos. A subtraction procedure is also applied in order to mitigate the effects of pile-up [84]. Finally, the R = 0.4 jets are further calibrated with additional correction factors derived in situ from a combination of γ+jet, Z+jet, and dijet-balance methods [83].
All jets reconstructed with the anti-k t algorithm using a radius parameter of R = 0.4 and a measured p jet T > 20 GeV are required to satisfy the quality criteria discussed in detail in Ref. [85]. These quality criteria selections for jets are extended to prevent contamination from detector noise through several detector-region-specific requirements. Jets contaminated by energy deposits due to noise in the forward hadronic endcap calorimeter are rejected and jets in the central region (|η| < 2.0) that are at least 95% contained within the EM calorimeter are required to not exhibit any electronic pulse shape anomalies [86]. Any event with a jet that fails these requirements is removed from the analysis.
Identification of jets containing b-hadrons (so-called b-jets) is achieved through the use of a multivariate b-tagging algorithm referred to as MV1 [87]. This algorithm is based on an artificial neural-network algorithm that exploits the impact parameters of charged-particle tracks, the parameters of reconstructed secondary vertices, and the topology of b-and c-hadron decays inside an anti-k t R = 0.4 jet. A working point corresponding to a 70% b-jet efficiency in simulated tt events is used. The corresponding mistag rates, defined as the fraction of jets originating from non-b-jets which are tagged by the b-tagging algorithm in an inclusive jet sample, for light jets and c-jets are approximately 1% and 20%, respectively. To account for differences with respect to data, data-derived corrections are applied to the MC simulation for the identification efficiency of b-jets and the probability to mis-identify jets resulting from light-flavour quarks, charm quarks, and gluons.
Initial jet-finding is extended using an approach called jet re-clustering [88]. This allows the use of largerradius jet algorithms while maintaining the calibrations and systematic uncertainties associated with the input jet definition. Small-radius anti-k t R = 0.4 jets with p T > 20 GeV and |η| < 2.4 are used as input without modification to an anti-k t R = 1.5 large-R jet algorithm, to identify the hadronic stop decays. The small-R jets with p T < 50 GeV are required to have a jet vertex fraction (JVF) of at least 50%. After summing the p T of charged-particle tracks matched to a jet, the JVF is the fraction due to tracks from the selected hard-scattering interaction and it provides a means by which to suppress jets from pile-up.
To further improve the background rejection, a splitting procedure is performed on each of the two leading large-R jets. After jet-finding, the constituents of these large-R jets -the anti-k t R = 0.4 input objects -are processed separately by the Cambridge-Aachen (C/A) algorithm [89,90], as implemented in FastJet 3. The C/A algorithm performs pair-wise recombinations of proto-jets (the inputs to the jet algorithm) purely based on their angular separation. Smaller-angle pairs are recombined first, thus the final recombined pair typically has the largest separation. The C/A final clustering is then undone by one step, such that there are two branches "a" and "b". The following splitting criteria are then applied to the branches "a" and "b" of each of the two leading large-R jets: • Both branches carry appreciable p T relative to the large-R jet: • The mass of each branch is small relative to its p T : If either of the leading two large-R jets fails these selections, the event is discarded. This implementation is identical to Ref.
[38], which is derived from the diboson-jet tagger [91]. This approach differs somewhat from that used in Ref. [92] in that no requirement is placed on the relative masses of the large-R and small-R jets.

Trigger and offline event selections
Events must satisfy jet and H T selections applied in the trigger which require H T = p T > 500 GeV, calculated as the sum of level-2 trigger jets within |η| < 3.2, and a leading jet within |η| < 3.2 with p T > 145 GeV. This relatively low-threshold jet trigger came online part-way through the data-taking period in 2012 and collected 17.4 fb −1 of data. The corresponding offline selections require events to have at least one anti-k t R = 0.4 jet with p T > 175 GeV and |η| < 2.4, as well as H T > 650 GeV, where the sum is over all anti-k t R = 0.4 jets with p T > 20 GeV, |η| < 2.4, and JVF > 0.5 if p T < 50 GeV. The cumulative trigger selection efficiency is greater than 99% for these offline requirements. The offline event preselection further requires that at least two large-R jets with p T > 200 GeV and mass > 20 GeV be present in each event. These requirements select a range of phase space for low stop masses in which the transverse momentum of the stops is often significantly greater than their mass.
The signal region (SR) is defined to suppress the large multijet background and to enhance the fraction of events that contain large-R jets consistent with the production of stop pairs, with each stop decaying to a light quark and a b-quark. Simulation studies indicate that three kinematic observables are particularly useful for background discrimination: 1. The mass asymmetry between the two leading large-R jets in the event (with masses m 1 and m 2 , respectively), defined as differentiates signal from background since the two stop subjet-pair resonances are expected to be of equal mass.
2. The (absolute value of the cosine of the) stop-pair production angle, | cos θ * |, with respect to the beam line in the centre-of-mass reference frame 3 distinguishes between centrally produced massive particles and high-mass forward-scattering events from QCD. It provides efficient discrimination and does not exhibit significant variation with the stop mass.
3. In addition, a requirement on the subjets is applied to each of the leading large-R jets in the event.
The p T of each subjet a and b relative to the other is referred to as the subjet p T2 /p T1 , defined by The A, | cos θ * |, and subjet p T2 /p T1 variables provide good discrimination between signal and background and are motivated by an ATLAS search for scalar gluons at √ s = 7 TeV [93] as well as by Refs. [38,94].
In addition to the kinematic observables described above, b-tagging applied to anti-k t R = 0.4 jets provides a very powerful discriminant for defining both the signal and the control regions, and one that is approximately uncorrelated with the kinematic features discussed above. Using these kinematic observables and the presence of at least two b-tagged jets per event, the signal region is defined by (for the leading two large-R jets) Distributions of the discriminating variables are shown in Figure 3. Insofar as the data points are dominated by background in these plots, even in the case of a potential signal, the data points should be understood to represent the background.
Following these selections, the distribution of the average mass of the leading two large-R jets, m jet avg = (m jet 1 + m jet 2 )/2, is used to search for an excess of events above the background prediction. The search is done in regions of m jet avg that are optimised to give the best significance. As shown in Figure 4, the stop signal is expected as a peak that would appear on top of a smoothly falling background spectrum. A Gaussian distribution is fitted to the stop signal m these mass windows and the signal efficiency in each window are given in Table 1. Figure 4(a) shows the mass windows overlaid on top of the signal m jet avg distributions for a few stop masses. The efficiency of the mass windows (relative to the SR cuts of Eq. (5)) varies from 79% at 100 GeV to 19% at 400 GeV. The low efficiency at high mass is due to the fact that the decay products are often not fully contained in the large-R jet, as can be seen in Figure 4(b). Figure 5 shows the product of acceptance and efficiency, after the SR cuts and mass windows, as a function of mt. The significantly lower acceptance times efficiency for light stop masses in Figure 5 is almost entirely due to the efficiency of the trigger selections which are for 100, 250, and 400 GeV stop masses 0.56%, 22%, and 96%, respectively. This low efficiency is compensated by the large cross section for low stop masses retaining sensitivity to these mass values.       Table 1, as a function of mt. The denominator of the efficiency (in %) is the total number of events, i.e. the top row in Table 3.

Background estimation
The estimation of the dominant SM multijet background in the signal region, including both the expected number of events and the shape of the m jet avg background spectrum, is performed directly from the data. MC simulations are used to study the background estimation method itself and to assess the contribution from tt production. For the background estimation, additional kinematic regions are defined by inverting the A and | cos θ * | selections as shown in Table 2. These are labelled An, Bn, Cn, where n indicates the number of b-tags (n = 0, = 1, ≥ 2). The signal region kinematic selection criteria of Eq. (5) are comprised by the Dn requirements and summarised in the last row of Table 2, where S R ≡ D2 with n ≥ 2 b-tags, and D1 with n = 1 b-tag is a validation region. Signal event yields are summarised in Table 3 for three stop masses.  The method relies on the assumption that the shape of the m jet avg spectrum is independent of the various b-tagging selections, as Figure 6(a) indicates, in each of the kinematic regions (An, Bn, Cn, and Dn) defined in Table 2. The advantage of the approach adopted here is that events with fewer than two btagged jets can be used as control and validation regions for in situ studies of these kinematic regions. An estimation of the normalisation and shape of the spectrum in the signal region D2 can therefore be tested and validated using events with n = 1 as well as regions A (A ≥ 0.1, | cos θ * | ≥ 0.3) and C (A ≥ 0.1, | cos θ * | < 0.3). Region B (A < 0.1, | cos θ * | ≥ 0.3) is primarily used to evaluate shape differences in the predicted m jet avg spectra (see Section 7.2). The A and | cos θ * | variables are found to have a correlation coefficient of at most 1% in data events for n = 0. In simulated multijet events, the correlation is also consistent with zero in events with n ≥ 2, within the large statistical uncertainties. Consequently, the ratio of n ≥ 2 (or n = 1) to n = 0 in regions A, B, and C should be approximately the same as the ratio in region D. The average jet mass spectrum, m jet avg , is compared across the various n selections for region A, as well as between each of the regions in events with n = 0. These comparisons are shown in Figure 6 along with the ratio of the spectrum in each region to that which most closely matches the final signal region in each figure (region D for n = 0 and n ≥ 2 for region A). The results demonstrate that the m jet avg spectra in regions C and D are reliably reproduced by regions A and B, respectively, as shown in Figure 6(b).
The potential for events from tt production to contribute increases with the addition of b-tag-multiplicity selections. Table 4 presents the number of events in the data and the contribution from tt, as determined Selection mt = 100 GeV mt = 250 GeV mt = 400 GeV Total events (9.72 ± 0.01) × 10 6 (9.54 ± 0.02) × 10 4 (6.202 ± 0.002) × 10 3 Jet + H T trigger (5.47 ± 0.08) × 10 4 (2.07 ± 0.01) × 10 4 (5.98 ± 0.02) × 10 3   All regions used for the background estimation (A0, C0, D0, A2, and C2) exhibit potential signal contribution of less than 10%. Region B2 (A < 0.1, | cos θ * | ≥ 0.3) is not used to derive the background estimate, since the expected signal contribution is much higher here than in A2 and C2 (for mt = 100 GeV the signal contribution is 50% in B2, compared with 2.2% in A2 and 8.2% in C2). The expected signal contribution in the validation regions (n = 1) is only significant in B1 and D1 (both require A < 0.1). Due to this level of expected signal contribution, and the m jet avg dependence of that contribution, the background estimation procedure obtains the m jet avg spectrum from the n = 0 regions for the final background spectrum estimate. The background estimation procedure itself is summarised in the following steps: the number of tt events is subtracted in regions A0, C0, A2, and C2 before evaluating the projection factor k A,C 2 : 3. The projection factor is used to estimate the total number of events, and shape (bin-by-bin), in the signal region, D2 (where the contribution from tt in D2 has been added).
This procedure is performed in the entire mass range and the mass windows are then defined from the estimated background spectrum. The projection factors k A2 and k C2 are compatible at the level of about 4% (including the tt subtraction as in Eq. (6)) and this difference is included as a systematic uncertainty on the background estimate (see Section 7). The validity of the background estimation method can be demonstrated in the n = 1 regions by deriving a projection factor analogously to Eq. (6) for n = 0 and n = 1, The expected number of events in the full range of D1 is then estimated by  Table 4: The observed event yields for 17.4 fb −1 in each of the regions for each b-tag multiplicity are shown, as well as the expected fractional signal contribution for the mass windows (as defined in Table 1) corresponding to mt = 100, 150, 175, and 400 GeV, and the tt contribution in the same mass windows. The tt systematic uncertainties include both the detector-level uncertainties and the theoretical uncertainties, as described in Section 7.
The same estimate for D2 gives In Eq. (10) and Eq. (11) the uncertainty quoted includes the statistical uncertainty and the uncertainties related to the tt estimate (see Section 7). These numbers should be compared with the observed numbers of events in Table 4, 12350 in D1 and 3688 in D2. The observed numbers of events are consistent with the estimated values.

Systematic uncertainties
Several sources of systematic uncertainty are considered when determining the estimated contributions from signal and background. The background estimate uncertainties pertain primarily to the method itself. The control and validation regions defined in Section 6 are used to evaluate the size of these uncertainties. A description of the primary sources of uncertainty follows. spectrum is used, as defined in Section 6). The b-jet-multiplicity m jet avg shape systematic uncertainty is calculated as the maximum of the bin-by-bin difference of region A2 compared to A0 (Figure 6(a)) and C2 compared to C0, where the normalised m jet avg spectrum are defined as ν Xn,i = N Xn,i /N Xn (X = A, C). The expression in Eq. (12) is then added in quadrature with the statistical uncertainty to form the total systematic uncertainty for that particular bin. A fixed bin width of 50 GeV is used in order to reduce effects due to statistical uncertainties. The size of the b-jet-multiplicity m jet avg shape systematic uncertainty varies from approximately 7-12% at low m jet avg to 20% near m jet avg ≈ 300 GeV, and to around 90% for m jet avg ≈ 400 GeV. The large systematic uncertainty in the high-mass tail is due to the low number of events in the n ≥ 2 regions. Figure 8 shows the b-jet-multiplicity m jet avg shape systematic uncertainty as well as the total systematic uncertainty when combined with the constant systematic uncertainty due to the 4% difference between projection factors k A2 and k C2 mentioned in Section 6, and the background estimation m jet avg shape systematic uncertainty described below in Section 7.2.

Background estimation m jet avg shape uncertainty
Events with n = 1 are used to test the validity of the background estimation method in data and to derive a systematic uncertainty on the approach. Figure 7 shows several results of this test by comparing three estimated spectra with the observed spectrum in each of the four regions. The estimated spectra of Figure 7 are determined using projection factors, from events with n = 0 to those with n = 1, in each of the three regions X = A, B, and C in order to determine the extent to which the prediction varies with each choice. Region D1 was used to validate the systematic uncertainty derived from A1, B1, and C1. Because of the three projection factors (k A , k B , and k C ) there are three estimates (N Y1 A ,i , N Y1 B ,i , and N Y1 C ,i ) of the m jet avg spectrum in each of the regions Y1 = A1, B1, and C1. Thus, in total there are nine estimates of the actual spectra, these are written succinctly as These estimates provide a test of the shape compatibility as well as the overall normalisation of the background estimate (the special cases N A1 A ,i , N B1 B ,i , and N C1 C ,i are normalised to the data by construction and thus only provide a shape comparison of n = 1 and n = 0). A systematic uncertainty for the background projection is then derived by taking, bin-by-bin, the largest deviation of the ratio of estimated to actual yield from unity in the m jet avg spectra in each of the regions A, B, and C according to where N Y1,i are the observed data points and N Y1 X ,i are the estimated spectra defined by Eq. (14). A bin width of 50 GeV is used, just as above with the b-jet multiplicity m jet avg shape systematic uncertainty. This is added in quadrature with the statistical uncertainty of that ratio in order to form the total systematic uncertainty for that particular bin. The size of the background estimation m jet avg shape systematic uncertainty varies from less than 10% at low m jet avg ≈ 100 GeV to 20% near m jet avg ≈ 400 GeV. Figure 8 shows the background estimation m jet avg shape systematic uncertainty as well as the total systematic uncertainty when combined with the two above-mentioned systematic uncertainties.  Bkg. est. shape syst.
-jet-multiplicity shape syst.  , and C1 to the actual spectra. The red dotted line represents the estimated systematic uncertainty due to shape differences between events with n = 0 and n ≥ 2. The green line represents a systematic uncertainty due to the level of compatibility of k A2 and k C2 . Finally, the black line with a filled yellow area shows the combined systematic uncertainty of all three contributions added in quadrature. The systematic uncertainty curves were smoothed with a Gaussian filter of spread 20 GeV.

Background tt contribution systematic uncertainty
Since POWHEG+PYTHIA MC simulation is used to determine the contribution from tt events in the signal region and each of the control regions, systematic uncertainties related to the MC simulation of the process itself are included in the total systematic uncertainty for the background estimation. The theoretical uncertainties include renormalisation and factorisation scale variations, parton distribution function uncertainties, the choice of MC generator using comparisons with MC@NLO [95], the choice of parton shower models using comparisons with Herwig [96], and initial-and final-state radiation (FSR) modelling uncertainties. The size of the theoretical systematic uncertainties for tt production vary from approximately 40% to 70% in the relevant kinematic regions and are dominated by the uncertainties from the MC generator and ISR/FSR variations. The detector-level uncertainties include the JES and JER uncertainties [83] as well as the b-tagging efficiency and mistag-rate uncertainties [87]. Uncertainties associated with the large-R jet mass scale and resolution are taken into account by the JES and JER uncertainties of the input small-R jets [88].
The size of the total tt systematic uncertainty varies in the mass range m jet avg = 100-200 GeV from approximately 50% to 80%. In the range m jet avg = 300-400 GeV the tt systematic uncertainties are of the order of 100%, but the tt background is completely negligible in this range. Lastly, an uncertainty of 2.8% is applied to the measured integrated luminosity of 17.4 fb −1 following the methodology described in Ref. [97].

Signal systematic uncertainties
In addition to the systematic uncertainties associated with the background estimate, the MC simulation of the signal model is subject to systematic uncertainties. Much like the contribution from tt, these uncertainties include experimental uncertainties as well as theoretical uncertainties. The detector-level uncertainties include the JES and JER uncertainties, and the b-tagging uncertainties as described for the estimate of tt. The theoretical uncertainties include renormalisation and factorisation scale variations, parton distribution function uncertainties, and ISR and FSR modelling uncertainties. The nominal signal cross-section and its uncertainty are taken from an envelope of cross-section predictions using different PDF sets and factorisation and renormalisation scales, as described in Ref. [66]. Each signal model is varied according to these systematic uncertainties and the impact on the acceptance in each mass window is then propagated to the final result. The largest contribution to the total signal systematic uncertainty comes from the JES and b-tagging, both in the range 10-18%. The size of the theoretical uncertainty grows from around 5% for low-mass stops to around 10% for higher-mass stops.
To evaluate the ISR/FSR systematic uncertainty, separate samples oftt * pair events are generated using MadGraph +PYTHIA, and the rate of ISR/FSR production is varied. These are used to reweight the p T (tt * ) distribution of the nominal signal samples to estimate the change in signal acceptance × efficiency. The effect ranges from 0-17%, with the largest impact at high mt. Table 5 summarises the observed and expected number of events that fall within each of the optimised mass windows in the signal region, D2. Figure 9 shows the observed m jet avg distribution in the data, along with the estimated background spectrum, including both the systematic and statistical uncertainties. No excess over the background prediction is observed.

Results
Model-independent upper limits at 95% confidence level (CL) on the number of beyond-the-SM (BSM) events for each signal region are derived using the CL s prescription [98] and neglecting any possible contribution in the control regions. Dividing these by the integrated luminosity of the data sample provides upper limits on the visible BSM cross-section, σ vis. , which is defined as the product of acceptance (A), reconstruction efficiency ( ), branching ratio (BR), and production cross-section (σ prod. ). This search specifically targets low-masst →bs decays, assuming 100% BR. The resulting limits on the number of BSM events and on the visible signal cross-section are shown in Table 6. The significance of an excess can be quantified by the probability (p 0 ) that a background-only experiment has at least as many events as observed. This p-value is also reported for each region in Table 6, where p 0 = 1 − CL b and CL b is the confidence level observed for the background-only hypothesis. The p-value is truncated at 0.5 for any signal region where the observed number of events is less than the expected number.  Table 5: Summary of the observed number of events in the data and the estimated number of signal and background events with total uncertainties (i.e. all listed uncertainties are the combined statistical and systematic uncertainties) that fall within each of the optimised mass windows in region D2. The total number of estimated background events in each window is the sum of the estimated background from the data-driven method and the tt simulation. The columns, from left to right indicate: N data-driven est.

B
, the data-driven background estimate; N tt est.

B
, the background contribution from tt; N tot. est.

B
, the total estimated background; N obs. data , the number of observed events in the data; and N S , the number of expected signal events.
Exclusion limits are set on the signal model of interest. A profile likelihood ratio combining Poisson probabilities for signal and background is computed to determine the 95% CL for compatibility of the data with the signal-plus-background hypothesis (CL s+b ) [99]. A similar calculation is performed for the background-only hypothesis (CL b ). From the ratio of these two quantities, the confidence level for the presence of signal (CL s ) is determined [98]. Systematic uncertainties are treated as nuisance parameters assuming Gaussian distributions and pseudo-experiments are used to evaluate the results. This procedure is implemented using a software framework for statistical data analysis, HistFitter [100]. The observed and expected 95% CL upper limits on the allowed cross-section are shown in Figure 10. For each simulated stop mass, the optimal mass window is chosen and the expected background yield is compared to the observed number of events in the mass window. Any potential signal contribution in the control regions from which the background estimates are derived is included as a systematic uncertainty on the background estimate. The size of the potential signal contribution in the control regions is shown for a few mass windows in Table 4. Stops with masses between 100 ≤ mt ≤ 315 GeV are excluded at 95% confidence level. All mass limits are quoted using thett * signal production cross-section reduced by one standard deviation of the theory uncertainties.    Obs. 95% CL limit Exp. 95% CL limit exp. limit σ 1 ± exp. limit σ 2 ±  The solid line with big round markers shows the observed limit, the dotted line shows the expected exclusion limit, and the green and yellow bands represent the uncertainties on this limit. Limits from the CDF Collaboration are shown in red for mt ≤ 100 GeV [40]. The blue line shows the theoretical signal cross-section and the blue band indicates the ±1σ variations due to theoretical uncertainties on the signal production crosssection given by renormalisation and factorisation scale and PDF uncertainties. For this search the cross-section is calculated at NLO+NLL, whereas in the CDF paper the cross-section was calculated at NLO only.

Conclusions
This paper presents a search for direct pair production of light top squarks, decaying via an R-parityviolating coupling to b-and s-quarks. This leads to a final state characterised by two large-radius hadronic jets that each contain both decay products of the top squark. The search uses 17.4 fb −1 of √ s = 8 TeV proton-proton collision data collected with the ATLAS detector at the LHC. No deviation from the background prediction is observed, and top squarks with masses between 100 and 315 GeV are excluded at 95% confidence level.

Acknowledgements
We thank CERN for the very successful operation of the LHC, as well as the support staff from our institutions without whom ATLAS could not be operated efficiently.

The ATLAS Collaboration
Johannesburg, South Africa