Search for top squark pair production in compressed-mass-spectrum scenarios in proton-proton collisions at sqrt(s) = 8 TeV using the alpha[T] variable

An inclusive search is performed for supersymmetry in final states containing jets and an apparent imbalance in transverse momentum, pt[miss], due to the production of unobserved weakly interacting particles in pp collisions at a centre-of-mass energy of 8 TeV. The data, recorded with the CMS detector at the CERN LHC, correspond to an integrated luminosity of 18.5 inverse femtobarns. The dimensionless kinematic variable alpha[T] is used to discriminate between events with genuine pt[miss] associated with unobserved particles and spurious values of pt[miss] arising from jet energy mismeasurements. No excess of event yields above the expected standard model backgrounds is observed. The results are interpreted in terms of constraints on the parameter space of several simplified models of supersymmetry that assume the pair production of top squarks. The search provides sensitivity to a broad range of top squark decay modes, including the two-body decay top squark to c chi0, where c is a charm quark and chi0 is the lightest neutralino, as well as the four-body decay top squark to b f f' chi0, where b is a bottom quark and f and f' are fermions produced in the decay of an intermediate off-shell W boson. These modes dominate in scenarios in which the top squark and lightest neutralino are nearly degenerate in mass. For these modes, top squarks with masses as large as 260 and 230 GeV are excluded, respectively, for the two- and four-body decays.


Introduction
The standard model (SM) is widely regarded as an effective approximation, valid at low energies, of a more complete theory of particle interactions, such as supersymmetry (SUSY) [1][2][3][4][5][6][7][8], which would supersede the SM at higher energy scales. A realisation of SUSY with TeVscale third-generation squarks is motivated by the cancellation of quadratically divergent loop corrections to the mass of the Higgs boson [9,10] avoiding the need for significant fine tuning [7,8,11]. In R-parity-conserving SUSY [12], supersymmetric particles (sparticles) such as squarks and gluinos are produced in pairs and decay to the lightest stable supersymmetric particle (LSP), which is generally assumed to be a weakly interacting and massive neutralino, χ 0 1 . A characteristic signature of these events is a final state with jets accompanied by an apparent, significant imbalance in transverse momentum, p miss T , due to unobserved χ 0 1 particles that can carry substantial momentum.
The lack of evidence to date for SUSY at the CERN LHC has led to the careful consideration of regions of the SUSY parameter space that have a relatively weak coverage in the experimental programme. One such class of models is that of compressed mass spectra, in which the LSP lies close in mass to the parent sparticle produced in the collisions. Models in which both the top squark ( t) and neutralino LSP are light and nearly degenerate in mass are phenomenologically well motivated [13][14][15][16][17][18][19][20]. For a mass splitting ∆m = m t − m χ 0 1 < m W , where m W is the mass of the W boson, the decay modes available to the top squark are either loop-induced, flavourchanging neutral current decays to a charm (c) quark and a neutralino, t → c χ 0 1 , or four-body decays, t → b ff χ 0 1 , where b is a bottom quark with f andf fermions from, for example, an off-shell W boson decay. Improved experimental acceptance for systems with compressed mass spectra can be achieved by requiring the sparticles to be produced in association with jets from initial-state radiation (ISR). The sparticle decay products from these systems can be Lorentz boosted to values of transverse momentum p T within the experimental acceptance if they recoil against a sufficiently high-p T jet from ISR. This topology is exploited by searches that consider "monojet" + p miss T final states [21][22][23]. The reliance on ISR is reduced for systems with larger ∆m, as in this case the sparticle decay products can have sufficiently large values of p T to lie within the experimental acceptance even without the Lorentz boost from ISR. This letter presents an inclusive search for the pair production of massive coloured sparticles in final states with two or more energetic jets and p miss T in pp collisions at √ s = 8 TeV. The data correspond to an integrated luminosity of 18.5 ± 0.5 fb −1 [24] collected with the CMS detector at the LHC. The search is based upon a kinematic variable α T , described in Section 3, which offers powerful discrimination against SM multijet production, and adheres to a strategy of maximising experimental acceptance through the application of loose selection requirements to provide sensitivity to a wide range of SUSY models. Previous versions of this search were reported at √ s = 7 TeV [25-27], and for an initial sample of data corresponding to 11.7 fb −1 at 8 TeV [28]. Other LHC searches for manifestations of SUSY in all-jet final states are presented in Refs. [21][22][23]. Recent searches for top squark production in leptonic final states can be found in Refs. [55] (and references therein) and [56,57].
The search makes use of the number of reconstructed jets per event (N jet ), the number of these jets identified as originating from b quarks (N b ), and the sum of the transverse energies of these jets (H T ), where the transverse energy of a jet is given by E T = E sin θ, with E the energy of the jet and θ its polar angle with respect to the beam axis. The three discriminants provide sensitivity to different production mechanisms of massive coloured sparticles at hadron colliders (i.e. squark-squark, squark-gluino, and gluino-gluino), to a large range of mass splittings between the parent sparticle and the LSP, and to third-generation squark signatures. While the search results can be interpreted with a broad range of models involving the strong production of coloured sparticles leading to final states with both low and high b quark content, we focus on the parameter space of simplified models [58][59][60] that assumes the pair production of top squarks, including the nearly mass-degenerate scenarios described above. Furthermore, interpretations are provided for top squarks that decay to the χ 0 1 either directly in association with a top quark ( t → t χ 0 1 ), or via an intermediate lightest chargino χ ± 1 in association with a bottom quark, with the subsequent decay of the χ ± 1 to the χ 0 1 and a W boson ( t → b χ ± 1 → bW ±( * ) χ 0 1 ). All models assume only the pair production of the low-mass eigenstate t 1 , with the t 2 decoupled to a high mass.
Several aspects of the present search are improved relative to the results of Ref. [28] in order to increase the sensitivity to models with nearly mass-degenerate t and χ 0 1 states. The signal region is extended to incorporate events with a low level of jet activity using a parked data set collected with a dedicated trigger stream [61], where "parked" means that, due to limitations in the available processing capability, the data were recorded without being processed through the reconstruction software, and were processed only subsequent to the end of the 2012 data collection period. Furthermore, tight requirements on a combination of kinematic variables are employed to suppress multijet production to the sub-percent level relative to the total remaining number of background events from other SM processes. Finally, an event veto based on isolated tracks is used to further suppress SM background contributions from τ → hadrons + ν decays and misreconstructed electrons and muons. These features yield an increased experimental acceptance to events with low jet activity, and improvements in the control of SM backgrounds, which are crucial for enhancing sensitivity to new sources of physics with nearly degenerate mass spectra.

The CMS detector
The central feature of the CMS detector is a superconducting solenoid providing an axial magnetic field of 3.8 T. The CMS detector is nearly hermetic, which allows for accurate momentum balance measurements in the plane transverse to the beam axis.
Charged particle trajectories are measured by a silicon pixel and strip tracker system, with full azimuthal (φ) coverage and a pseudo-rapidity acceptance |η| < 2.5. Isolated particles of p T = 100 GeV emitted at |η| < 1.4 have track resolutions of 2.8% in p T and 10 (30) µm in the transverse (longitudinal) impact parameter [62].
A lead tungstate crystal electromagnetic calorimeter (ECAL) and a brass and scintillator hadron calorimeter (HCAL) surround the tracking volume and provide coverage over |η| < 3.0. A forward HCAL extends the coverage to |η| < 5.0. In the barrel section of the ECAL, an energy resolution of about 1% is achieved for unconverted or late-converting photons with energies on the order of several tens of GeV. In the η-φ plane, and for |η| < 1.48, the HCAL cells map onto 5 × 5 arrays of ECAL crystals to form calorimeter towers projecting radially outwards from a location near the nominal interaction point. At larger values of |η|, the size of the towers increases and the matching ECAL arrays contain fewer crystals. Within each tower, the energy deposits in ECAL and HCAL cells are summed to define the calorimeter tower energies, subsequently used to provide the energies and directions of reconstructed jets. The HCAL, when combined with the ECAL, measures jet energies with a resolution of approximately 40% at 12 GeV, 5% at 100 GeV, and 4% at 1 TeV.
Muons are identified in gas ionisation detectors embedded in the steel flux-return yoke of the magnet. Muons are measured in the range |η| < 2.4. By matching track segments recon-structed in the muon detectors to segments measured in the silicon tracker, a relative transverse momentum resolution of 1.3-2.0% and <10% is achieved for muons with, respectively, 20 < p T < 100 GeV and p T < 1 TeV [63].
The first level (L1) of the CMS trigger system, composed of custom hardware processors, uses information from the calorimeters and muon detectors to select events of interest within a fixed time interval of less than 4 µs. The high-level trigger (HLT) processor farm further decreases the event rate from around 100 kHz to about 600 Hz, before data storage. Of these events, about half are reconstructed promptly. The other half represent the parked data set referred to above.
A more detailed description of the CMS detector, together with a definition of the coordinate system used and the relevant kinematic variables, can be found in Ref. [64].

The α T variable
The α T kinematic variable, first introduced in Refs. [25,65], is used to efficiently reject events that do not contain significant p miss T or that contain large p miss T only because of transverse momentum mismeasurements, while retaining sensitivity to new-physics events with significant p miss T . The α T variable depends solely on the transverse energies and azimuthal angles of jets, and is intrinsically robust against the presence of jet energy mismeasurements in multijet systems.
For events containing only two jets, α T is defined as T is the transverse energy of the jet with smaller E T , and M T is the transverse mass of the dijet system, defined as: where E j i T , p j i x , and p j i y are, respectively, the transverse energy and x or y components of the transverse momentum of jet j i . For a perfectly measured dijet event with E j 1 T = E j 2 T and the jets in the back-to-back configuration (∆φ = π), and in the limit in which the momentum of each jet is large compared with its mass, the value of α T is 0.5. For an imbalance in the E T values of the two back-to-back jets, whether due to an over-or under-measurement of the E T of either jet, then E j 2 T < 0.5M T . This in turn implies α T < 0.5, giving the variable its intrinsic robustness. Values of α T significantly greater than 0.5 are observed when the two jets are not back-to-back and recoil against significant, genuine p miss T from weakly interacting particles that escape the detector, such as neutrinos.
The definition of the α T variable can be generalised for events with more than two jets [25]. The mass scale for any process is characterised through the scalar E T sum of jets, defined as where N jet is the number of jets with E T above a predefined threshold. The estimator for | p miss T | is given by the magnitude of the vector p T sum of all the jets, defined by H miss For events with three or more jets, a pseudo-dijet system is formed by combining the jets in the event into two pseudo-jets. The total H T for each of the two pseudo-jets is given by the scalar E T sum of its contributing jets. The combination chosen is the one that minimises ∆H T , defined as the difference between the H T of the two pseudo-jets. This clustering criterion assumes a balanced-momentum hypothesis, | p miss T | ≈ 0 GeV, which provides the best separation between SM multijet events and events with genuine p miss T . The α T definition can then be generalised to: When jet energies are mismeasured, or there are neutrinos from heavy-flavour quark decays, the magnitude of H miss T and ∆H T are highly correlated. This correlation is much weaker for R-parity-conserving SUSY events, where each of the two decay chains produces an undetected LSP.

Event reconstruction and selection
The event reconstruction and selection criteria described below are discussed in greater detail in Ref. [28]. To suppress SM processes with genuine p miss T from neutrinos, events containing an isolated electron [66] or muon [63] with p T > 10 GeV are vetoed. Furthermore, events containing an isolated track [67] with p T > 10 GeV are vetoed. Events containing isolated photons [68] with p T > 25 GeV are also vetoed to ensure an event sample comprising only multijet final states.
Jets are reconstructed from the energy deposits in the calorimeter towers, clustered using the anti-k T algorithm [69] with a radius parameter of 0.5. The jet energies measured in the calorimeters are corrected to account for multiple pp interactions within an event (pileup), and to establish a uniform relative response in η and a calibrated absolute response in p T [70]. Jets are identified as originating from b quarks using the "medium" working point of the combined secondary vertex algorithm [71], such that the probability to misidentify jets originating from light-flavour partons (gluons and u, d, or s quarks) as b quark jets is approximately 1% for jets with p T = 80 GeV. The "medium" working point results in a b-tagging efficiency, i.e. the probability to correctly identify jets as originating from b quarks, in the range 60-70% depending on the jet p T .
All jets are required to satisfy |η| < 3.0, and the jet with largest E T is also required to satisfy |η| < 2.5. All jets and the two jets with largest E T are, respectively, subjected to a nominal (E T > 50 GeV) and higher (E T > 100 GeV) threshold. Events are required to contain at least two jets that satisfy the aforementioned E T and η requirements. The value of H T for each event is determined from these jets. If H T < 375 GeV, the respective jet E T thresholds are lowered to 43 and 87 GeV, H T is recalculated, and the event is reconsidered for selection. If the recalculated H T is less than 325 GeV, the respective E T thresholds are lowered yet further, to 37 and 73 GeV and H T again recalculated. If this newly recalculated H T is less than 200 GeV, the event is rejected. The scheme is summarised in Table 1. Events can be selected with this iterative procedure even if they do not satisfy the sets of tighter requirements on the E T thresholds. The reason why lower jet E T thresholds are employed for 200 < H T < 375 GeV is to maintain a similar background composition in all H T bins, and to increase the acceptance for SUSY models characterised by compressed mass spectra. Significant jet activity in the event is established by requiring H T > 200 GeV, which also ensures high efficiency for the trigger conditions, described below, used to record the events. Events are vetoed if rare, anomalous signals are identified in the calorimeters [72] or if any jet satisfies E T > 50 GeV and has |η| > 3, in order to enhance the performance of H miss T as an estimator of | p miss T |.
Events are categorised according to the number of jets per event, 2 ≤ N jet ≤ 3 or N jet ≥ 4, and the number of reconstructed b quark jets per event, N b = 0, 1, 2, 3, or ≥4. For events containing exactly zero or one b quark jet, we employ eleven bins in H T : three bins at low jet  Table 3.
For events satisfying the above selection criteria, the multijet background dominates over all other SM sources. Multijet events populate the region α T 0.5, and the α T distribution is characterised by a sharp edge at 0.5, beyond which the multijet event yield falls by several orders of magnitude. Multijet events with extremely rare but large stochastic fluctuations in the calorimetric measurements of jet energies can lead to values of α T slightly above 0.5. The edge at 0.5 sharpens with increasing H T for multijet events, primarily due to a corresponding increase in the average jet energy and a consequent improvement in the jet energy resolution. The contribution from multijet events is suppressed by more than five orders of magnitude by imposing the H T -dependent α T requirements summarised in Table 1.
Several beam-and detector-related effects, such as interactions from beam halo, reconstruction failures, detector noise, or event misreconstruction due to detector inefficiencies, can lead to events with large, unphysical values of p miss T and values of α T greater than 0.55. These types of events are rejected with high efficiency by applying a range of vetoes [73].
Two final event vetoes complete the definition of the signal region. An estimator for p miss T is defined by the negative of the vector sum of the transverse momenta of all reconstructed particles in an event, as determined by the particle-flow (PF) algorithm [74,75]. The magnitude of this vectorial summation is referred to as E miss T . The first veto concerns the rare circumstance in which several jets, collinear in φ and each with p T below its respective threshold, result in significant H miss T . This type of background, typical of multijet events, is suppressed while maintaining high efficiency for SM or new-physics processes with genuine p miss T by requiring H miss T /E miss T < 1.25. The second veto considers the minimum azimuthal separation between a jet and the negative of the vector sum derived from the transverse momenta of all other jets in the event, which is referred to as ∆φ * min [25]. This variable is employed to suppress potential contributions from energetic multijet events that have significant p miss T through the production of neutrinos in semileptonic heavy-flavour decays. Such neutrinos are typically collinear with the axis of a jet. We impose the requirement ∆φ * min > 0.3, which effectively suppresses this background as determined using control data.

Triggers and data control samples
Candidate signal events are recorded under multiple jet-based trigger conditions that require both H T and α T to satisfy predetermined thresholds. The trigger-level jet energies are corrected to account for energy scale and pileup effects. The trigger efficiencies for the SM backgrounds are measured using a sample of µ + jets events, which provides an unbiased coverage of the kinematic phase space when the muon is ignored. The efficiencies are determined as a function of N jet and H T , and lie in the range 79-98% and >99% for 200 < H T < 375 GeV and H T > 375 GeV, respectively. The inefficiencies at low values of H T , which are accounted for in the final result, arise from conditions imposed on L1 trigger quantities. Statistical uncertainties of a few percent are considered. Simulation-based studies demonstrate that trigger inefficiencies for signal events are typically negligible.
A set of prescaled H T trigger conditions is used to record events for a multijet-enriched control sample, defined by relaxed requirements on α T , ∆φ * min , and H miss T /E miss T with respect to the signal region. This event sample is used to estimate the multijet background contribution.
Significant background in the signal region is expected from SM processes with genuine p miss T in the final state. The dominant processes are the associated production of W or Z bosons and jets, with the decays Z → νν or W ± → ν ( = e, µ, τ), and top quark pair production followed by semileptonic top quark decay. Three separate data control regions are used to estimate the background from these processes. The control regions are defined through the selection of µ + jets, µµ + jets, or γ + jets events [28]. The selection criteria are chosen such that the SM processes and their kinematic properties resemble as closely as possible the SM background behaviour in the signal region, once the muon, dimuon system, or photon are ignored in the determination of quantities such as H T and α T . The event selection criteria are defined to ensure that the potential contribution from multijet events or from a wide variety of SUSY models (i.e. so-called signal contamination) is negligible. Events are categorised according to N jet , N b , and H T , identically to the scheme used for events in the signal region, as defined in Section 4.
The µ + jets sample is recorded using a trigger that requires an isolated muon. The event selection criteria are chosen so that the trigger is maximally efficient (≈90%). Furthermore, the muon is required to be well separated from the jets in the event, and the transverse mass formed by the muon and E miss T system must lie between 30 and 125 GeV to ensure a sample rich in W bosons (produced promptly or from the decay of top quarks). The µµ + jets sample uses the same trigger condition (efficiency ≈99%) and similar selection criteria as the µ + jets sample, specifically requiring two oppositely charged isolated muons that are well separated from the jets in the event, and with a dilepton invariant mass within a ±25 GeV window around the nominal mass of the Z boson. For both the muon and dimuon samples, no requirement is made on α T , in order to increase the statistical precision of the predictions from these samples. The γ + jets events are recorded using a single-photon trigger condition. The event selection criteria require an isolated photon with p T > 165 GeV, H T > 375 GeV, and α T > 0.55, yielding a trigger efficiency of 99%.

Multijet background suppression
The signal region is defined in a manner to suppress the expected contribution from multijet events to the sub-percent level relative to the expected background from other SM processes for all event categories and H T bins. This is achieved through very restrictive requirements on the α T and ∆φ * min variables, as described above. In this section, we discuss these requirements further, together with the procedure for estimating the remaining multijet background.
Independent estimates are determined per bin in the signal region, defined in terms of N jet , N b , and H T . The method utilises the multijet-enriched control sample introduced in Section 5, defined by 0.505 < α T < 0.55 and no threshold requirements on ∆φ * min or H miss T /E miss T . The event counts in this data sideband are corrected to account for contamination from nonmultijet processes, which are estimated using the method described in Section 7. The method exploits the evolution of the ratio R(α T ), defined by the number of (corrected) event counts that satisfy the requirement H miss T /E miss T < 1.25 to the number that fail, as a function of α T . The ratio R(α T ) is observed to monotonically fall as a function of α T and is modelled, independently for each bin, with an exponential function F (α T ). An additional multijet-enriched data sideband, defined by H miss T /E miss T > 1.25 and α T > 0.55, is used to determine the number of (corrected) events N (α T > α min T ) per bin that satisfy a minimum threshold requirement on α T . Finally, an estimate of the multijet background for each bin is determined as a function of the threshold α min T based on the product of N (α T > α min T ) and the extrapolated value of the ratio from the corresponding fit, F (α T > α min T ). The α T value required to suppress the predicted multijet contribution to the sub-percent level relative to the total SM background is determined independently for each bin of the signal region. The α min T thresholds determined from this method are summarised in Table 1 and, for simplicity, are chosen to be identical for all N jet and N b categories. Higher α T thresholds are required than those used for Ref.
[28] because of higher pileup conditions in the latter half of the data collected in 2012 and because of the addition of the low H T bins.
Various checks are performed in simulation and in data to assure closure, which, in simulation refers to the ability of the method to correctly predict the background rates found in simulated data, and, in data, refers to the consistency between the data-derived predictions for, and counts in, a separate multijet-enriched validation sample in data. The exponential functions are found to adequately model the observed behaviour in data and simulation. Systematic uncertainties in the predictions are obtained from the differences observed using alternative fit functions and can be as large as ∼100%.
Following application of the α T requirements, residual contributions from multijet events with significant p miss T due to semileptonic heavy-flavour decays are suppressed by requiring ∆φ * min > 0.3, as discussed in Section 4. This suppression is validated in simulation and in data using a control sample defined by the requirements H T > 775 GeV and either 0.51 < α T < 0.55 or H miss T /E miss T > 1.25. These events are selected with an unprescaled H T trigger, allowing a study of the performance of the selection requirements in the low α T region around 0.51, which corresponds to similar H miss T values as employed in the lowest H T bins. From these studies, the remaining multijet background is found to be at the sub-percent level. With this level of suppression, any residual contribution from multijet events is assumed to be negligible compared to the uncertainties associated with the nonmultijet backgrounds (described below) and is ignored.

Estimation of nonmultijet backgrounds
In events with few jets or few b quark jets, the largest backgrounds are Z → νν + jets or W ± → ν + jets. At higher jet or b quark jet multiplicities, tt and single top production also become an important source of background. For W boson decays that yield an electron or muon (possibly originating from leptonic τ decays), the background arises when the e or µ is not rejected through the dedicated lepton vetoes. Background also arises when the τ lepton decays to neutrinos and hadrons, which are identified as a jet. The veto of events containing at least one isolated track is efficient at further suppressing these backgrounds, including those from single-prong τ-lepton decays, by as much as ∼50% for categories enriched in tt.
The production of W and Z bosons in association with jets is simulated with the leading-order (LO) MADGRAPH 5.1.1.0 [76] event generator, with up to four additional partons considered in the matrix element calculation. The production of tt and single top quark events is generated  with the next-to-leading-order (NLO) POWHEG 1.0 [77][78][79][80] program. The LO PYTHIA 6.4.26 [81] program is used to generate WW, WZ, and ZZ (diboson) events, and to describe parton showering and hadronisation for all samples. The CTEQ6L1 [82] and CT10 [83] parton distribution functions (PDFs) are used with MADGRAPH and POWHEG, respectively. The description of the detector response is implemented using the GEANT4 [84] package. The simulated samples are normalised by the most accurate cross section calculations currently available, usually up to next-to-next-to-leading-order (NNLO) accuracy in QCD [85][86][87][88][89]. To model the effects of pileup, the simulated events are generated with a nominal distribution of pp interactions per bunch crossing and then reweighted to match the pileup distribution measured in data. Figure 1 shows the distributions of the α T variable obtained from samples of events that satisfy the selection criteria used to define the µ + jets control region and the signal region. The inclusive requirements N jet ≥ 2, N b ≥ 0, and H T > 200 and 375 GeV for the two samples, respectively, are imposed. The distributions illustrate the background composition of the two samples as determined from simulation. While the figure also demonstrates an adequate modelling of the α T variable with simulated events, the method employed by the search to estimate the nonmultijet backgrounds is designed to mitigate the effects of simulation mismodelling.
The method relies on the use of transfer factors that are constructed per bin, with a binning scheme defined identically to that of the signal region in terms of N jet , N b , and H T , for each control sample in data. The transfer factors are determined using simulated events, and are given by the ratios of the expected yields in the corresponding bins of the signal region and control samples. The transfer factors are used to extrapolate from the event yield measured in a data control sample to the expectation for background from a particular SM process or processes in the signal region. The method aims to minimise the effects of simulation mismodelling, as many systematic biases are expected to largely cancel in the ratios used to define the transfer factors. Uncertainties in the transfer factors are determined from a data-derived approach, described below.
The µ + jets data sample provides an estimate of the total contribution from tt and W boson production, as well as of the residual contributions from single top quark, diboson, and Drell-Yan (qq → Z/γ * → + − ) production. Two independent estimates of the background from Z → νν + jets events with N b ≤ 1 are determined, one from the γ + jets data sample and the other from the µµ + jets data sample, which are considered simultaneously in the likelihood function described in Section 8. The γ + jets and Z → µµ + jets processes have similar kinematic properties when the photon or muons are ignored in the determination of E miss T and H miss T [90], although the acceptances differ. An advantage of the γ + jets process is its much larger production cross section compared to the Z → νν + jets process.
In the case of events with N b ≥ 2, the µ + jets sample is also used to estimate the small Z → νν + jets background because of the limited event counts in the µµ + jets and γ + jets control samples. The method relies on the use of W → µν + jets events to predict the Z → νν + jets background [25, 27, 28]. The method corrects for tt contamination in the µ + jets sample, which can be significant in the presence of jets identified as originating from b quarks. However, while the tt contamination increases with increasing N b , the Z → νν + jets background is reduced to a subdominant level relative to other backgrounds. The method is validated in data control regions defined by samples of events categorised according to N b . In summary, only the µ + jets sample is used to estimate the total SM background for events with N b ≥ 2, whereas all three data control samples are used for events with N b ≤ 1.
To maximise sensitivity to new-physics signatures with a large number of b quarks, a method is employed that allows event yields for a given b quark jet multiplicity to be predicted with a higher statistical precision than obtained directly from simulation, particularly for events with a large number of b quark jets (N b ≥ 2) [28]. The method relies on generator-level information contained in the simulation to determine the distribution of N b for a sample of events categorised according to N jet and H T . First, simulated events are categorised according to the number of jets per event that are matched to underlying b quarks (N gen b ), c quarks (N gen c ), and light-flavoured quarks or gluons (N gen q ). Second, the efficiency with which b quark jets are identified, and the misidentification probabilities for c quarks and light-flavour partons, f c and f q , respectively, are also determined from simulation, with each quantity averaged over jet p T and η per event category. Corrections to , f c , and f q are applied on a jet-by-jet basis as a function of p T and η so that they match the corresponding quantity measured in data [71].   Figure 2: Ratio (N obs − N pred )/N pred as a function of H T for different event categories and/or control regions for (upper) events with two or three jets, and (lower) events with four or more jets; "b tag" refers to a reconstructed b quark candidate. Error bars represent statistical uncertainties only, while the grey shaded bands represent the N jet -and H T -dependent uncertainties assumed in the transfer factors, as determined from the procedure described in the text.
Systematic uncertainties are determined from core sets of closure tests, of which the results are shown in Fig. 2. Five sets of tests are performed independently for each of the two N jet categories, and a further three sets that are common to both N jet categories. The tests aim to probe for the presence of statistically significant biases that could arise due to limitations in the method. For each N jet category, the first three sets of closure tests are performed using the µ + jets sample. The first set probes the modelling of the α T distribution for events containing genuine p miss T from neutrinos (open circle markers). Two sets (crosses, squares) probe the relative composition between W + jets and top events and the modelling of the reconstruction of b quark jets. The fourth set (triangles) validates the modelling of vector boson production by connecting the µ + jets and µµ + jets control samples, which are enriched in W + jets and Z + jets events, respectively. The fifth set (swiss crosses) deals with the consistency between the γ + jets and µµ + jets samples, which are both used to provide an estimate of the Z → νν + jets background. Three further sets of closure tests (stars, inverted triangles, diamonds), one per data control sample, probe the simulation modelling of the N jet distribution for a range of background compositions. The closure tests reveal no significant biases or dependency on N jet nor H T . Systematic uncertainties in the transfer factors are determined from the variance in (N obs − N pred )/N pred , weighted to account for statistical uncertainties, for all closure tests within an individual H T bin in the range 200 < H T < 375 GeV and for each N jet category. For the region H T > 375 GeV, all tests within 200 GeV-wide intervals in H T , defined by pairs of adjacent bins, are combined to determine the systematic uncertainty, which is assumed to be fully correlated for bins within each interval, and fully uncorrelated for different H T intervals and N jet categories. The magnitudes of the systematic uncertainties are indicated by shaded grey bands in Fig. 2 and summarised in Table 2. The same (uncorrelated) value of systematic uncertainty is assumed for each N b category. An independent study is performed to assess the effect of uncertainties in the simulation modelling of the efficiency and misidentification rates for jets originating from b quarks and from light-flavoured quarks or gluons. These uncertainties are found to be at the sub-percent level, subdominant relative to the values in Table 2, and therefore considered to be negligible.

Results and interpretation
For a given category of events satisfying requirements on both N jet and N b , a likelihood model of the observations in all data samples is used to obtain a consistent prediction of the SM backgrounds and to test for the presence of a variety of signal models. This is written as: where L SR = ∏ i Pois(n i | b i + s i ) is a likelihood function comprising a product of Poisson terms that describe the yields in each of the H T bins of the signal region for given values of N jet and N b . In each bin of H T (index i), the observation n i is modelled as a Poisson variable distributed about the sum of the SM expectation b i and a potential contribution from a signal model s i (assumed to be zero in the following discussion). The contribution from multijet production is assumed to be zero, based on the studies described in Section 6. The SM expectations in the  signal region are related to the expected yields in the µ + jets, µµ + jets, and γ + jets control samples via the transfer factors derived from simulation. Analogous to L SR , the likelihood functions L µ , L µµ , and L γ describe the yields in the H T bins of the µ + jets, µµ + jets, and γ + jets control samples for the same values of N jet and N b as the signal region. For the category of events with N b ≥ 2, only the µ + jets control sample is used in the likelihood to determine the total contribution from all nonmultijet SM backgrounds in the signal region. The systematic uncertainties in the transfer factors, determined from the ensemble of closure tests described above and with magnitudes in the range 4-26% (Table 2), are accommodated in the likelihood function through a nuisance parameter associated with each transfer factor used in the background estimation for each (N jet , N b ) category and H T interval. The H T intervals are defined by pairs of adjacent H T bins for the region H T > 375 GeV, as described in Section 7, and so adjacent bins share the same nuisance parameter. The measurements of these parameters are assumed to follow a lognormal distribution. Table 3 summarises the observed event yields and expected number of events from SM pro-cesses in the signal region as a function of N jet , N b , and H T . The "a priori" SM expectations are determined from event counts in the data control samples and transfer factors from simulation, and are therefore independent of the signal region. No significant discrepancies are observed between the "a priori" SM expectations and the observed event yields. In addition, a simultaneous fit to data in the signal region and in up to three control regions is performed.
The likelihood function is maximised over all fit parameters under the SM-only hypothesis in order to estimate the yields from SM processes in each bin in all regions, in the absence of an assumed contribution from signal events. Table 3 summarises these estimates (labelled "SM") for the signal region. A goodness-of-fit test is performed to quantify the degree of compatibility between the observed yields and the expectations under the background-only hypothesis. The test is based on a log likelihood ratio and the alternative hypothesis is defined by a "saturated" model [91]. The p-value probabilities for all N jet and N b categories are found to be uniformly distributed, with a minimum value of 0.19.
The results of this search are interpreted in terms of limits on the parent sparticle and LSP masses in the parameter space of simplified models [58][59][60] that represent the direct pair production of top squarks and the decay modes t → c χ 0 [92,93] is used to determine upper limits at the 95% confidence level (CL) on the production cross section of a signal model, using the onesided (LHC-style) profile likelihood ratio as the test statistic [94]. The sampling distributions for the test statistic are generated from pseudo-experiments using the respective maximum likelihood values of nuisance parameters determined from a simultaneous fit to the pseudodata, in the 75 bins of the signal region and in the corresponding bins of up to three control samples, under the SM background-only and signal + background hypotheses. The potential contributions of signal events to each of the signal and control samples are considered, but the only significant contribution occurs in the signal region and not the control samples.
The event samples for the simplified models are generated with the LO MADGRAPH 5.1.1.0 generator, which considers up to two additional partons in the matrix element calculation. Inclusive, process-dependent, NLO calculations of SUSY production cross sections, with nextto-leading-logarithmic (NLL) corrections, are obtained with the program PROSPINO 2.1 [95][96][97][98][99][100]. All events are generated using the CTEQ6L1 PDFs. As for SM processes, the simulated events are generated with a nominal pileup distribution and then reweighted to match the distribution observed in data. The detector response is provided by the CMS fast simulation package [101].
Experimental uncertainties in the expected signal yields are considered. Contributions to the overall systematic uncertainty arise from various sources such as the uncertainties from the choice of PDFs, the jet energy scale, the modelling of the efficiency and misidentification probability of b quark jets in simulation, the integrated luminosity [24], and various event selection criteria. The magnitude of each contribution depends on the model, the masses of the parent sparticle and LSP, and the event category under consideration. Uncertainties in the jet energy scale are typically dominant (∼15%) for models with mass splittings that satisfy ∆m > m t , where m t is the top quark mass. The acceptance for models with mass splittings satisfying ∆m < m t is due in large part to ISR, the modelling of which contributes the dominant systematic uncertainty for systems with a compressed mass spectrum. An uncertainty of ∼20% is determined by comparing the simulated and measured p T spectra of the system recoiling against the ISR jets in tt events, using the technique described in Ref. [67]. For the aforementioned simplified models, the effect of uncertainties in the distribution of signal events is generally small compared with the uncertainties in the experimental acceptance. The total systematic uncertainty in the yield of signal is found to be in the range 5-36%, depending on N jet and N b , and is taken into account through a nuisance parameter that follows a lognormal distribution. Figure 3 shows the observed upper limit on the production cross section at 95% confidence level (CL), as a function of the top squark and χ 0 1 masses, for a range of simplified models based on the pair production of top squarks, together with excluded mass regions. Figures 3 (upper left and right) show the sensitivity of this analysis to the decay modes t → c χ 0 1 and t → b ff χ 0 1 , respectively. Models with ∆m as small as 10 GeV are considered, and the top squarks are assumed to decay promptly. The excluded regions are determined using the NLO+NLL cross sections for top squark pair production, assuming that b squarks, lightflavoured squarks, and gluinos are too heavy to be produced in the pp collisions. Also shown are the excluded regions observed when the production cross section is changed by its theoretical uncertainty, and the expected region of exclusion, as well as those determined for both ±1 and ±2 standard deviation (σ) changes in experimental uncertainties. The range of excluded top squark masses is sensitive to both the decay mode and ∆m. For the decay t → c χ 0 1 , the expected excluded region is relatively stable as a function of ∆m, with t masses below 285 and 325 GeV excluded, respectively, for ∆m = 10 and 80 GeV. The observed exclusion, assuming the theoretical production cross section reduced by its 1σ uncertainty, is weaker, with t masses below 240 and 260 GeV excluded for ∆m = 10 and 80 GeV. For the decay t → b ff χ 0 1 , the expected excluded mass region is strongly dependent on ∆m, weakening considerably for increasing values of ∆m due to the increased momentum phase space available to leptons produced in the four-body decay. Top squark masses below 265 and 165 GeV are excluded based on the expected results, respectively, for ∆m = 10 and 80 GeV. The observed exclusion is again weaker, with masses below 225 and 130 GeV excluded. The nonsmooth behaviour of the exclusion contours is the result of statistical fluctuations and the sparseness of the scan over the mass parameter space, and does not represent a kinematical effect. Figures 3 (middle left and right) show the limits on the allowed cross section for the decay t → b χ ± 1 , followed by a decay of the χ ± 1 to the χ 0 1 and to either an on-or off-shell W boson, depending on the mass difference between the χ ± 1 and χ 0 1 . For a model with m χ ± 1 = 0.25m t + 0.75m χ 0 1 , shown in Fig. 3 (middle left), the analysis has sensitivity in the region m χ ± 1 − m χ 0 1 < m W , excluding χ 0 1 masses up to 225 GeV and t masses up to 350 GeV. Models that satisfy m χ ± 1 < 91.9 GeV, or m χ ± 1 < 103.5 GeV and m χ ± 1 − m χ 0 1 < 5 GeV, are already excluded by a combination of results obtained from the ALEPH, DELPHI, L3, and OPAL experiments at LEP [102,103]. For a model with m χ ± 1 = 0.75m t + 0.25m χ 0 1 , shown in Fig. 3 (middle right), t masses up to 400 GeV can be excluded but the reach in χ 0 1 mass is reduced. Figure 3 (lower left) shows the results of the analysis for the decay t → t χ 0 1 . Both two-and threebody decays are considered, for which the latter scenario involves an off-shell top quark. The polarizations of the top quarks are model dependent and are non-trivial functions of the topsquark and neutralino mixing matrices [104]. Simulated events of the production and decay of top squark pairs are generated without polarization of the top quarks. Models with m t < 200 GeV are not considered, due to significant signal contributions in the control regions. Top squark masses up to 500 GeV are excluded, and χ 0 1 masses up to 100 and 50 GeV are excluded for the two-and three-body decays, respectively. As in Fig. 3 (middle right), the observed limit is around 2σ below the expected result for large values of m t . This is mainly due to an excess of observed counts in data in the N b = 2 categories in the region of 500 < H T < 700 GeV, which is compatible with a statistical fluctuation. The observed limits lie closer to the expected values at low top squark masses, which correspond to lower values of H T for which good agreement between the data and SM background predictions is observed.     plane. The sensitivity for these models is typically driven by categories involving events satisfying N jet ≥ 4 and 1 ≤ N b ≤ 2, while events with lower N jet and N b multiplicities become increasingly important for nearly mass-degenerate models.

Summary
An inclusive search for supersymmetry with the CMS detector is reported, based on data from pp collisions collected at √ s = 8 TeV, corresponding to an integrated luminosity of 18.5 ± 0.5 fb −1 . The final states analysed contain two or more jets with large transverse energies and a significant imbalance in the event transverse momentum, as expected in the production and decay of massive squarks and gluinos. Dedicated triggers made it possible to extend the phase space covered in this search to values of H T and H miss T as low as 200 and 130 GeV, respectively. These regions of low H T and H miss T correspond to regions of phase space that are highly populated in models with low-mass squarks and nearly degenerate mass spectra. The signal region is binned according to H T , the number of reconstructed jets, and the number of jets identified as originating from b quarks. The sum of standard model backgrounds in each bin is estimated from a simultaneous binned likelihood fit to the event yields in the signal region and in µ + jets, µµ + jets, and γ + jets control samples. The observed yields in the signal region are found to be in agreement with the expected contributions from standard model processes.
Limits are determined in the mass parameter space of simplified models that assume the direct pair production of top squarks. A comprehensive study of top squark decay modes is performed and interpreted in the parameter space of the loop-induced two-body decays to the neutralino and one c quark ( t → c χ 0 1 ); four-body decays to the neutralino, one b quark, and an off-shell W boson ( t → b ff χ 0 1 ); decays to one b quark and the lightest chargino ( t → b χ ± 1 ), followed by the decay of the chargino to the lightest neutralino and an (off-shell) W boson; and the decay to a top quark and neutralino ( t → t χ 0 1 ). In the region m t − m χ 0 1 < m W , top squarks with masses as large as 260 and 225 GeV, and neutralino masses up to 240 and 215 GeV, are excluded, respectively, for the two-and four-body decay modes. For top squark decays to b χ ± 1 , top squark masses up to 400 GeV and neutralino masses up to 225 GeV are excluded, depending on the mass of the chargino. For top squarks decaying to a top quark and a neutralino, top squark masses up to 500 GeV and neutralino masses up to 105 GeV are excluded.
In summary, the analysis provides sensitivity across a large region of parameter space in the (m t , m χ 0 1 ) plane, covering several relevant top squark decay modes. In particular, the application of low thresholds to maximise signal acceptance provides sensitivity to models with compressed mass spectra. For top squark decays to b χ ± 1 , where the W boson from the χ ± 1 decay is off-shell, the presented studies improve on existing limits. Mass exclusions are reported in previously unexplored regions of the (m t , m χ ± 1 , m χ 0 1 ) parameter space that satisfy 100 GeV < ∆m < m t , of up to m t = 325, m χ ± 1 = 250, and m χ 0 1 = 225 GeV. For the region ∆m < m W , the search provides the strongest expected mass exclusions, up to m t = 325 GeV, for the two-body decay t → c χ 0 1 when 30 GeV < ∆m < m W .
institutes for their contributions to the success of the CMS effort. In addition, we gratefully acknowledge the computing centres and personnel of the Worldwide LHC Computing Grid for delivering so effectively the computing infrastructure essential to our analyses. Finally, we acknowledge the enduring support for the construction and operation of the LHC and the CMS detector provided by the following funding agencies: