Search for supersymmetry in hadronic final states with missing transverse energy using the variables AlphaT and b-quark multiplicity in pp collisions at 8 TeV

An inclusive search for supersymmetric processes that produce final states with jets and missing transverse energy is performed in pp collisions at a centre-of-mass energy of 8 TeV. The data sample corresponds to an integrated luminosity of 11.7 inverse femtobarns collected by the CMS experiment at the LHC. In this search, a dimensionless kinematic variable, AlphaT, is used to discriminate between events with genuine and misreconstructed missing transverse energy. The search is based on an examination of the number of reconstructed jets per event, the scalar sum of transverse energies of these jets, and the number of these jets identified as originating from bottom quarks. No significant excess of events over the standard model expectation is found. Exclusion limits are set in the parameter space of simplified models, with a special emphasis on both compressed-spectrum scenarios and direct or gluino-induced production of third-generation squarks. For the case of gluino-mediated squark production, gluino masses up to 950-1125 GeV are excluded depending on the assumed model. For the direct pair-production of squarks, masses up to 450 GeV are excluded for a single light first- or second-generation squark, increasing to 600\GeV for bottom squarks.


Introduction
The standard model (SM) of particle physics has been extremely successful in describing phenomena at the highest energies attained thus far. Nevertheless, it is widely believed to be only an effective approximation of a more complete theory that would supersede the SM at a higher energy scale. Supersymmetry (SUSY) [1][2][3][4][5][6][7][8] is generally regarded as one of the likely extensions to the SM. The theory is based on the unique way to extend the space-time symmetry group underpinning the SM, introducing a relationship between fermions and bosons.
A low-energy realisation of SUSY, e.g. at the TeV scale, is motivated by the cancellation of the quadratically divergent loop corrections to the Higgs boson mass in the SM [7,8]. In order to avoid a large amount of fine-tuning in these loop corrections, the difference in masses between the top quark and the third-generation squarks must not be too large [9]. While the majority of SUSY particles (sparticles) may be beyond the reach of the Large Hadron Collider (LHC) at the present beam energy and luminosity, the recent discovery of a low-mass Higgs boson candidate [10,11] motivates "natural" SUSY models in which top and bottom squarks (and gluinos) appear at the TeV scale. For R-parity-conserving SUSY [12], sparticles will be produced in pairs and decay to SM particles and the lightest sparticle (LSP), which is generally assumed to be weakly interacting and massive. Therefore, the pair production of massive coloured sparticles is expected to result in a signature that is rich in jets, in particular those originating from bottom quarks if the third-generation squarks are light, and contains a significant amount of missing transverse energy, E T / , due to the undetected LSPs.
This paper summarises an inclusive search for pair production of massive coloured sparticles in final states with jets and E T / , performed in pp collisions at a centre-of-mass energy √ s = 8 TeV. The analysed data sample corresponds to an integrated luminosity of 11.7 ± 0.5 fb −1 [13] collected by the Compact Muon Solenoid (CMS) experiment. Several other searches in this channel have been conducted by both the ATLAS and CMS experiments [14][15][16][17][18][19][20][21][22][23][24][25][26]. The strategy of the analysis presented in this paper is based on the kinematic variable α T , which provides powerful discrimination against multijet production, a manifestation of quantum chromodynamics (QCD), while maintaining sensitivity to a wide range of SUSY models. This analysis extends previous searches based on a similar strategy with samples of pp collisions at √ s = 7 TeV [24][25][26].
In order to improve the sensitivity of the analysis to the main production mechanisms of massive coloured sparticles at hadron colliders (squark-squark, squark-gluino, and gluino-gluino), events with significant E T / and two or more energetic jets are categorised according to the jet multiplicity. Events with two or three reconstructed jets are used to search for squark-squark and squark-gluino production, while events with four or more reconstructed jets probe gluinogluino production. This classification according to the jet multiplicity is a new feature with respect to the previous analysis [24]. Moreover, to enhance the sensitivity to third-generation squark signatures, events are further categorised according to the number of reconstructed jets identified as originating from bottom quarks (b-quark jets). The analysis also considers a large dynamic range in the scalar sum of the transverse energies of reconstructed jets in order to probe signal models over a large range of mass splittings between the parent sparticle and the LSP, including models characterised by a compressed spectrum [27]. This approach provides sensitivity to a wide variety of SUSY event topologies arising from the pair production and decay of massive coloured sparticles while still maintaining the character of an inclusive search.

Interpretation with simplified models
To interpret the results of this search, simplified models [28][29][30] are used. These effective models include only a limited set of sparticles (production and decay) to enable comprehensive studies of individual SUSY event topologies. The result of this search can also be interpreted in a range of other relevant models, such as the constrained minimal supersymmetric extension of the standard model (CMSSM) [31][32][33] or other effective or complete SUSY models that predict event topologies with two or more energetic jets and significant E T / .
In this paper, we focus on the interpretation in two classes of simplified models, the first of which describes direct pair production of squarks, including top and bottom squarks, that decay to a quark of the same flavour and the LSP. The second class describes gluino-induced production of (off-shell) squarks, again including top and bottom squarks, in which gluino pair production is followed by the decay of each gluino to a quark-antiquark pair and the LSP. The simplified models considered in this analysis are summarised in Table 1. For each model, the LSP is assumed to be the lightest neutralino. Table 1 also defines reference models in terms of the parent (gluino or squark) and LSP sparticle masses, m parent and m LSP , respectively, which are used to illustrate potential yields in the signal region. In the case of the model D3, a massless LSP is considered. The masses are chosen to be reasonably high while still being within the expected sensitivity reach. Table 1: A summary of the simplified models considered in this analysis, which involve both direct (D) and gluino-induced (G) production of squarks, and their decays. Models D1 and G1 concern the direct or gluino-induced production of first-or second-generation squarks only. Reference models are also defined in terms of the parent (gluino or squark) and LSP sparticle masses.

The CMS apparatus
The central feature of the CMS apparatus is a superconducting solenoid of 6 m internal diameter, providing a magnetic field of 3.8 T. Within the superconducting solenoid volume are a silicon pixel and strip tracker, an electromagnetic calorimeter (ECAL) comprising 75 848 leadtungstate crystals, and a brass/scintillator hadron calorimeter (HCAL). Muons are measured in gas-ionisation detectors embedded in the steel flux return yoke of the magnet. Extensive forward calorimetry complements the coverage provided by the barrel and endcap detectors. The CMS detector is nearly hermetic, which allows for momentum balance measurements in the plane transverse to the beam axis.
CMS uses a right-handed coordinate system, with the origin at the nominal interaction point, . ( 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 T and jets back-to-back in φ, 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 the case of an imbalance in the measured transverse energies of back-to-back jets, α T is reduced to a value smaller than 0.5, which gives the variable its intrinsic robustness with respect to jet energy mismeasurements. A similar behaviour is observed for energetic dijet events that contain neutrinos from the decay of a bottom or charm quark, as the neutrinos are typically collinear with respect to the axis of the heavy-flavour jet. Values significantly greater than 0.5 are observed when the two jets are not back-to-back and are recoiling against significant, genuine E T / .
The definition of the α T variable can be generalised for events with two or more jets as follows. The mass scale of the physics processes being probed is characterised by the scalar sum of the transverse energy E T of jets considered in the analysis, defined as where n jet is the number of jets with E T above a predefined threshold. The estimator for E T / is given by the magnitude of the transverse momenta p T vectorial sum over these jets, defined as 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 E T for each of the two pseudo-jets is calculated as the scalar sum of the measured E T of the contributing jets. The combination chosen is the one that minimises the absolute E T difference between the two pseudo-jets, ∆H T . This simple clustering criterion provides the best separation between multijet events and events with genuine E T / . Equation (1) can therefore be generalised as: In the presence of jet energy mismeasurements or neutrinos from heavy-flavour quark decays, the direction and magnitude of the apparent missing transverse energy, H / T , and energy imbalance of the pseudo-dijet system, ∆H T , are highly correlated. This correlation is much weaker for R-parity-conserving SUSY with each of the two decay chains producing the LSP.

Physics objects
Jets are reconstructed from the energy deposits in the calorimeter towers [37], clustered by the infrared-safe anti-k T algorithm [38] with a size parameter of 0.5. In this process, the contribution from each calorimeter tower is assigned a momentum, the absolute value and the direction of which are given by the energy measured in the tower and the position of the tower. The raw jet energy is obtained from the sum of the tower energies and the raw jet momentum by the vectorial sum of the tower momenta, which results in a nonzero jet mass. The raw jet energies are corrected to remove the effects of overlapping pp collisions (pileup) [39,40] and to establish a relative uniform response of the calorimeter in η and a calibrated absolute response in p T .
The presence of a b-quark jet is inferred by the Combined Secondary Vertex algorithm [41] that incorporates several measurements to build a single discriminating variable that can be used to identify jets originating from bottom quarks with high efficiency and purity. Due to the pixeldetector acceptance, b-quark jets are identified only in the region |η| < 2.4. In this analysis, the discriminator threshold is chosen such that the probability to misidentify (mistag) jets originating from light-flavour partons (u, d, s quarks or gluons) as b-quark jets is approximately 1% for jets with transverse momenta of 80 GeV [41]. This threshold results in a b-tagging efficiency, i.e. the probability to correctly identify jets as originating from bottom quarks, in the range 60-70% [41], dependent on jet p T .
The reconstruction of photons, electrons and muons is described below. The presence (or absence) of these objects is used to define the event samples for the signal and multiple control regions, the latter of which are used to estimate the background contributions from SM processes in the signal region.
The energy of photons [42] is directly obtained from the ECAL measurement, corrected for zero-suppression and pileup effects. Various identification criteria must be met in order to correctly identify photons with high efficiency and suppress the misidentification of electrons, jets, or spurious ECAL noise as photons. These include the requirements that the shower shape of the energy deposition in the ECAL be consistent with that expected from a photon, the energy detected in the HCAL behind the photon shower must not exceed 5% of the photon energy, and no matched hits in the pixel tracker must be found. Isolation from other activity in the event is determined through a combination of independent energy sums obtained from each of the HCAL, ECAL, and tracker subdetectors within a cone of ∆R = (∆φ) 2 + (∆η) 2 = 0.3 around the photon trajectory. These sums are corrected for pileup effects and for the contributions from the photon itself.
The energy of electrons [43] is determined from a combination of the track momentum at the main interaction vertex, the corresponding ECAL cluster energy, and the energy sum of all bremsstrahlung photons attached to the track. Identification criteria similar to those described above for photons are applied, with additional requirements on the associated track that consider the track quality, energy-momentum matching, and compatibility with the main interaction vertex in terms of the transverse and longitudinal impact parameters.
The energy of muons [44] is obtained from the corresponding track momentum, combining measurements from the muon detectors and both the silicon pixel and strip tracking subdetectors. Various track quality criteria are considered when identifying muons, as are the transverse and longitudinal impact parameters with respect to the main interaction vertex.
Isolation of muons and electrons is based on a combination of independent sums from the HCAL, ECAL, and tracker subdetectors and measured relative to the muon or electron transverse momentum. The isolation sums are determined for a cone of radius ∆R = 0.3 (0.4) around the electron (muon) trajectory and are corrected for the effects of pileup and for the contributions from the lepton itself.

Event selection for the signal region
Events containing non-collision backgrounds are suppressed by requiring at least one vertex of high-p T tracks to be reconstructed in the luminous region. In the case of multiple vertices, the main interaction vertex is defined as the one with the highest scalar sum of p T 2 of all associated tracks.
In order to suppress SM processes with genuine E T / from neutrinos in the final state, events are vetoed if they contain an isolated electron or muon with p T > 10 GeV. Events with an isolated photon with p T > 25 GeV are also vetoed to ensure an all-jet final state.
Jets are required to have transverse energy E T > 50 GeV and |η| < 3.0. The two highest-E T jets must each satisfy E T > 100 GeV. These two E T requirements are relaxed for some signal regions, as described below. The highest-E T jet is additionally required to satisfy |η| < 2.5. Events are vetoed that contain rare, spurious signals from the calorimeters [45] that are misidentified as jets. To ensure that the variable H / T is an unbiased estimator of E T / , events are vetoed if any additional jet satisfies both E T > 50 GeV and |η| > 3.
Events are required to have H T > 275 GeV to ensure high efficiency for the trigger conditions used to record the event sample, described in Section 4.4. The signal region is divided into eight bins in H T : two bins of width 50 GeV in the range 275 < H T < 375 GeV, five bins of width 100 GeV in the range 375 < H T < 875 GeV, and a final open bin, H T > 875 GeV. As in Ref. [26], the jet E T threshold is scaled down to 37 and 43 GeV for the regions 275 < H T < 325 and 325 < H T < 375 GeV, respectively. The threshold for the two highest-E T jets is also scaled accordingly to 73 and 87 GeV. This is done in order to maintain a background composition similar to that observed for the higher H T bins, and also to increase the analysis acceptance for SUSY models characterised by compressed spectra.
Events are further 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 the category of events satisfying n jet ≥ 4 and n b ≥ 4, the six highest H T bins are combined to give a final open bin of H T > 375 GeV.
For events satisfying the selection criteria described above, the multijet background dominates over all other SM backgrounds. As discussed in Section 4.1, multijet events populate the region α T < 0.5. 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 thus an improvement in the jet energy resolution. This effect yields an exponential dependence on H T for the ratio of multijet events with a value of α T above and below a given threshold value (larger than 0.5), as described further in Section 6.
The contribution from multijet events is suppressed by many orders of magnitude by requiring α T > 0.55. As an example, an event that satisfies both H T = 275 (875) GeV and α T = 0.55 must also satisfy H / T ≥ 115 (365) GeV. However, certain classes of rare background events can lead to values of α T greater than 0.55, such as those containing beam halo, reconstruction failures, spurious detector noise, or event misreconstruction due to detector inefficiencies. These event classes, with large, non-physical values of E T / , are rejected by applying dedicated vetoes [36], the most important of which are described below.
The first example concerns events containing severe energy mismeasurements as a result of jets being reconstructed within or near to inefficient regions in the ECAL (which amount to ∼1% of the ECAL channel count) or the instrumentation gap between the ECAL barrel and endcap systems at |η| = 1.48. These events are identified and vetoed as follows. The negative vector sum of jet transverse momenta when jet j is ignored, defined as − ∑ n jet i=1,i =j p T i , is determined for each ignored jet in turn, 1 ≤ j < n jet . An azimuthal distance of ∆φ < 0.5 between the directions of jet j and the corresponding vector sum indicates that jet j has suffered a sufficiently large energy mismeasurement to satisfy α T > 0. 55. The event is rejected if the angular distance in the (η, φ) plane between the affected jet and the closest inefficient ECAL region satisfies ∆R < 0.3. Similarly, the event is rejected if the η position of the affected jet satisfies ∆η < 0.3 with respect to the ECAL barrel-endcap boundary.
The second example concerns the rare circumstance in which several jets with transverse energies below the E T thresholds and aligned in φ result in significant H / T relative to the value of E T / (which is less sensitive to jet E T thresholds). This type of background, typical of multijet events, is suppressed while maintaining high efficiency for SM or new physics processes with genuine, significant E T / by requiring H / T /E T / < 1.25. The measurement of E T / is provided by the particle-flow (PF) reconstruction framework [46,47]. Figure 1 shows the α T distributions of events with H T > 375 GeV that satisfy all the selection criteria described above except the α T requirement, categorized according to n jet . An inclusive set of trigger conditions is used in order to show the full α T distribution. The analysis relies on data control samples to estimate the contributions from the multijet and non-multijet backgrounds, as described in Sections 5 and 6. However, for illustration, the expected yields from simulation of multijet events, non-multijet backgrounds with genuine E T / , the sum of these SM backgrounds, and an example signal model, are also shown in Fig. 1. The expected yield for multijet events that satisfy α T > 0.55, as given by simulation, is less than ten events and is negligible with respect to all other SM backgrounds. Figure 1 highlights the ability of the α T variable to discriminate between multijet events and all other SM or new physics processes with genuine E T / in the final state.  Figure 1: The α T distributions of events with H T > 375 GeV that satisfy all the selection criteria described above except the α T requirement, categorised according to 2 ≤ n jet ≤ 3 (left) and n jet ≥ 4 (right). An inclusive set of trigger conditions is used to collect the events in data (black solid circles with error bars). Expected yields as given by simulation are also shown for multijet events (green dash-dotted line), non-multijet backgrounds with genuine E T / as described in

Trigger conditions
Events are recorded with multiple jet-based trigger conditions, implemented on the HLT computing farm, that require both H T and α T to lie above predetermined thresholds, as summarised in Table 2. Different trigger conditions are used depending on the analysis H T bin. The triggerlevel jet energies are corrected to account for scale and pileup effects. The thresholds used in the H T binning scheme are shifted up by 25 GeV with respect to the trigger thresholds in order to maintain high efficiency for the H T component of the trigger condition.
The trigger efficiency, defined as the probability with which events that satisfy the signal region selection criteria also satisfy the trigger condition, is measured from data for each n jet category. The efficiency is measured using a data sample of µ + jets events recorded by an independent and unbiased trigger condition that requires an isolated muon satisfying p T > 24 GeV and |η| < 2.1. The muon is required to be well separated from the nearest jet j by requiring ∆R(µ, j) > 0.5 and is ignored in the calculation of H T and α T in order to emulate a genuine E T / signature.
The measured efficiencies are summarised in Table 2. Non-negligible inefficiencies, which are accounted for in the final result, are observed only for the lowest H T bin. The HLT-based trigger conditions are dependent on multiple requirements on quantities determined by the L1 trigger logic, which include combinations of scalar sums of jet E T measurements and individual E T thresholds on sub-leading jets. The different efficiencies measured for the two n jet categories in the lowest H T bin are a result of the requirements on L1 trigger quantities that exhibit nonnegligible inefficiencies at very low H T .

Dominant background processes
In the absence of a significant contribution from multijet events, the remaining backgrounds in the signal region stem from SM processes with significant E T / in the final state.
For events in which no b-quark jets are identified, the largest backgrounds are from the production of W and Z bosons in association with jets. The decay Z → νν is the only relevant contribution from Z + jets events. For W + jets events, the two relevant sources are leptonic decays, in which the lepton is not reconstructed or fails the isolation or acceptance requirements, and the decay W → τν in which the τ decays hadronically and is identified as a jet.
For events satisfying n b ≥ 1, tt production followed by semileptonic decays becomes the most important background process. For the subset of events satisfying n b = 1 and 2 ≤ n jet ≤ 3, the total contribution from the W + jets and Z + jets backgrounds is comparable to the tt background; otherwise tt production dominates. Events with three or more reconstructed b-quark jets originate almost exclusively from tt events, in which one or several jets are misidentified as b-quark jets.
Residual contributions from single-top-quark and diboson production are also expected.

Definition of the data control samples
Three independent data control samples, binned identically to the signal region, are used to estimate the contributions from the various background processes. These samples are defined by a selection of µ + jets, µµ + jets, and γ + jets events. The event selection criteria for these control samples are defined to ensure that any potential contamination from multijet events is negligible. Furthermore, the selections are also expected to suppress contributions from a wide variety of SUSY models (signal contamination) to a negligible level. The selection criteria that define the three data control samples are chosen such that the composition of background processes and their kinematic properties resemble as closely as possible those of the signal region once the muon, dimuon system, or photon are ignored when computing quantities such as H T , ∆H T , H / T , and α T . This approach emulates the effects, including misreconstruction and acceptance, that lead to the presence of these background processes in the signal region.
The µ + jets sample is recorded using a trigger condition that requires an isolated muon satisfying p T > 24 GeV and |η| < 2.1. The event selection requires exactly one isolated muon that satisfies stringent quality criteria, p T > 30 GeV, and |η| < 2.1 in order for the trigger to be maximally efficient at (88.0 ± 2.0)%. Furthermore, the transverse mass of the muon and E T / [46, 47] system must be larger than 30 GeV to ensure a sample rich in W bosons. The muon is required to be separated from the closest jet in the event by the distance ∆R > 0.5. The event is rejected if two muon candidates are identified that have an invariant mass within a window of ±25 GeV around the mass of the Z boson, regardless of the quality and isolation of the second muon candidate. No selection requirement on α T is made in order to increase the statistical precision of the predictions derived from this sample, while the impact of removing the α T requirement is tested with a dedicated set of closure tests described in Section 5.4.
The µµ + jets sample uses the same trigger condition as the µ + jets sample. Events are selected by requiring exactly two oppositely charged, isolated muons that satisfy stringent quality criteria and |η| < 2.1. The highest-p T and lowest-p T muons must satisfy p T > 30 GeV and p T > 10 GeV, respectively. The invariant mass of the di-muon system is required to be within a window of ±25 GeV around the mass of the Z boson. Both muons are required to be separated from their closest jets in the event by the distance ∆R > 0.5. Again, no requirement on α T is made. These selection criteria lead to a trigger efficiency of 95 ± 2%, rising to 98 ± 2% with increasing H T .
The γ + jets sample is selected using a dedicated photon trigger requiring a localised, large energy deposit in the ECAL with E T > 150 GeV that satisfies loose photon identification and isolation criteria [42]. The offline selection requires H T > 375 GeV, α T > 0.55, and a single photon to be reconstructed with E T > 165 GeV, |η| < 1.45, satisfying tight isolation criteria, and with a minimum distance to any jet of ∆R > 1.0. For these selection criteria, the photon trigger condition is found to be fully efficient.

Method
The method used to estimate the non-multijet backgrounds in the signal region relies on the use of transfer factors, which are constructed per data control sample in bins of H T , n jet , and n b . These transfer factors are determined from simulated event samples, which are produced as follows. The production of W and Z bosons in association with jets is simulated with the MAD-GRAPH V5 [48] event generator. The production of tt and single-top quark events is generated with POWHEG [49], and diboson events are produced with PYTHIA 6.4 [50]. For all simulated samples, PYTHIA 6.4 is used to describe parton showering and hadronisation. The description of the detector response is implemented using the GEANT4 [51] package. The simulated samples are normalised using the most accurate cross section calculations currently available, usually with next-to-leading-order (NLO) accuracy. 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 as measured in data.
Each transfer factor is defined as the ratio of expected yields as given by simulation in a given bin of the signal region, N signal MC , and the corresponding bin of one of the control samples, N control MC . Each transfer factor is then used to extrapolate from the event yield measured in a data control sample, N control obs , to an expectation for the event yield in the corresponding bin of the signal region, N signal pred , via the expression: Two independent estimates of the irreducible background of Z → νν + jets events are determined from the data control samples comprising Z → µµ + jets and γ + jets events, both of which have similar kinematic properties when the muons or photon are ignored [52] but different acceptances. Of the γ + jets and Z → µµ + jets processes, the former has a larger production cross section while the latter has kinematic properties that are more similar to Z → νν + jets.
The µ + jets data sample provides an estimate for the total contribution from all other SM processes, which is dominated by tt and W-boson production. Residual contributions from single-top-quark and diboson production are also estimated. For the category of events satisfying n b ≥ 2, in which the contribution from Z → νν + jets events is suppressed to a negligible level, the µ + jets sample is also used to estimate this small contribution rather than using the statistically limited µµ + jets and γ + jets samples. Hence, only the µ + jets sample is used to estimate the total SM background for events satisfying n b ≥ 2, whereas all three data control samples are used for events satisfying n b ≤ 1.
In order to maximise sensitivity to potential new physics signatures in final states with multiple b-quark jets, a method that improves the statistical power of the predictions from simulation, particularly for n b ≥ 2, is employed. The distribution of n b is estimated from generator-level information contained in the simulation. The number of reconstruction-level jets matched to underlying bottom quarks (n gen b ), charm quarks (n gen c ), and light-flavoured partons (n gen q ) per event, N(n gen b , n gen c , n gen q ), is recorded in bins of H T for each n jet category. The b-tagging efficiency, , and mistag probabilities, f c and f q , are also determined from simulation for each H T bin and n jet category, with each quantity averaged over jet p T and η. Corrections are applied on a jet-by-jet basis to both , f c , and f q in order to match the corresponding measurements from data [41]. This information is sufficient to predict n b and thus also determine the event yield N(n b ) from simulation for a given H T bin and n jet category with the expression: where n tag b , n tag c , and n tag q are the number of times that a reconstructed b-quark jet is identified as originating from an underlying bottom quark, charm quark, or light-flavoured parton, respectively, and P b ≡ P(n The predicted yields are found to be in good statistical agreement with the yields obtained directly from the simulation in the bins with a significant population. The method exploits the ability to make precise measurements of N(n gen b , n gen c , n gen q ), , f c , and f q independently of n b , which means that event yields for a given b-quark jet multiplicity can be predicted with a higher statistical precision than obtained directly from simulation. Precise measurements of f c and f q are particularly important for events with n b ≥ 3, which often occur in the SM because of the presence of mistagged jets in the event. In this case, the largest background is tt, with two correctly tagged b-quark jets and an additional mistagged jet originating from a charm quark or light-flavoured parton.

Systematic uncertainties on transfer factors
As described in Section 5.3, the method to estimate the background contributions from SM processes with significant E T / is based on an extrapolation from a measurement in a control sample to a yield expectation in the signal region. This approach aims to minimise the sensitivity to simulation mismodelling, as many systematic biases are expected largely to cancel in the ratios used to define the transfer factors. However, a systematic uncertainty is assigned to each transfer factor to account for theoretical uncertainties [52] and residual biases in the simulation modelling of kinematics (e.g. acceptances) and instrumental effects (e.g. reconstruction inefficiencies).
The magnitudes of the systematic uncertainties assigned to the transfer factors are determined from a representative set of closure tests in data. These tests use yields from an event category in one of the three independent data control samples, along with the corresponding transfer factors obtained from simulation, to predict the yields in another event category or data control sample following the prescription defined in Eq. (4). As stated previously, the contamination from multijet events or any potential signal is expected to be negligible. Therefore, the closure tests carried out between control samples probe the properties of the relevant SM non-multijet backgrounds.
Thirteen sets of closure tests are chosen to probe key ingredients of the simulation modelling that may introduce biases in the transfer factors. Each set comprises up to eight independent tests in bins of H T . Five sets of closure tests are performed independently for each of the two n jet categories, and a further three sets are common to both categories, as shown in Fig. 2. For each n jet category, the first three sets of closure tests are carried out within the µ + jets sample, and probe the modelling of the α T distribution in genuine E T / events (circles), the relative composition between W + jets and top events (squares), and the modelling of the reconstruction of b-quark jets (triangles), respectively. The fourth set (crosses) addresses the modelling of the vector boson samples by connecting the µ + jets and µµ + jets control samples, with the former sample rich in W + jets events (and also with a significant contribution from top events) and the latter in Z + jets events. The fifth set (solid bullets) deals with the consistency between the Z → µµ + jets and γ + jets samples, which are both used to provide an estimate of the Z → νν + jets background. Three further sets of closure tests (inverted triangles, diamonds, asterisks), one per data control sample, probe the simulation modelling of the n jet distribution.
All sets of closure tests demonstrate, given the statistical precision of each test, that there are no significant biases or dependencies on H T exhibited by the transfer factors obtained from simulation. Table 3 summarises the results obtained from constant and linear polynomial fits to each set of closure tests for the two n jet categories. The table also lists the best fit values and uncertainties for the constant polynomial fits, which indicate the level of closure averaged across the full H T range considered in the analysis. All tests are either statistically compatible   with zero bias or at the level of a few percent or less. Finally, Table 3 also summarises the best fit values of the slopes of the linear polynomial fits, which are typically of the order 10 −4 , corresponding to a percent-level change per 100 GeV. However, in all cases, the best fit values are fully compatible with zero, indicating that the level of closure is H T -independent. The χ 2 and number of degrees of freedom (dof) of each fit are also quoted and indicate a reasonable goodness-of-fit in all cases except one, which concerns the simulation modelling of the n jet distribution in the µ + jets sample. The large χ 2 value is mainly attributable to a single outlier in the bin 675 < H T < 775 GeV rather than any significant trend in H T . Once it is established that no significant bias or trend is observed for any set of closure tests, uncorrelated systematic uncertainties on the transfer factors are determined for five independent regions in H T : 275-325, 325-375, 375-575, 575-775, and ≥ 775 GeV. Conservative estimates for the systematic uncertainties are based on the variance in the level of closure for all individual tests, weighted according to the statistical uncertainties associated with each test, within a given H T region. This procedure yields estimates of 10% (10%), 10% (10%), 10% (10%), 20% (20%), and 20% (30%) for the five H T regions defined above for events satisfying 2 ≤ n jet ≤ 3 (n jet ≥ 4), as indicated by the shaded bands in Fig. 2.
The effect on the transfer factors of uncertainties related to the modelling of b-quark jets in simulation is studied in detail. After correcting the b-tagging efficiency and mistag probability determined in simulation for residual differences as measured in data, the corresponding uncertainties on these corrections are propagated to the transfer factors. In addition, several robustness tests are performed, e.g. treating c-quark jets as b-quark jets. While the absolute yields

Estimating the multijet background
The contribution from multijet events is expected to be negligible, at or below the percentlevel relative to the yields expected from non-multijet backgrounds, even for the most inclusive definition of the signal region, defined by H T > 275 GeV, α T > 0.55, and no requirement on n jet or n b . The expected yield is further suppressed to 1 event with the application of more stringent thresholds on any of the variables H T , n jet , or n b .
Any potential contamination from multijet events via the effects described in Sections 4.1 and 4.3 can be estimated by exploiting the H T dependence of the ratio of events with a value of α T above and below some threshold, R α T (H T ). This dependence on H T is modelled as a falling exponential function, R α T (H T ) = Ae −kH T [26], where the parameters A and k are the normalisation and decay constant parameters, respectively. The exponential model is validated in a multijet-enriched data sideband, defined by the event selection criteria for the signal region, described in Section 4.3, but with the requirement H / T /E T / > 1. 25. A measurement of the decay constant k is made in a further multijet-enriched sample defined by the event selection criteria for the signal region but with the requirement α T < 0.55.
The estimate of the multijet contamination in the signal region for a given H T bin is determined from the product of the ratio R α T , as given by the exponential model, and the yield in a data control sample defined by the event selection for the signal region but with the requirement α T < 0.55. This event sample is recorded with a set of trigger conditions that require only H T to be above the same thresholds as used by the signal region triggers listed in Table 2.
Further details on the exponential model and its use in the likelihood model are found in Section 7.

Confronting data with the SM-only hypothesis
For a given category of events satisfying requirements on both n jet and n b , a likelihood model of the observations in multiple 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. It is written as: where L SR describes the yields in the eight H T bins of the signal region where exactly n jet jets and n b b-quark jets are required. In each bin of H T , the observation is modelled as a Poissondistributed variable about the sum of the SM expectation and a potential signal contribution (assumed to be zero in the following discussion), where the SM expectation is the sum of the multijet and non-multijet components. The non-multijet component is related to the expected yields in the µ + jets, µµ + jets, and γ + jets control samples via the transfer factors derived from simulation, as described in Section 5.3. 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 in the same category of n jet and n b as the signal region. For the category of events satisfying n b ≥ 2, only the µ + jets control sample is used in the likelihood to determine the total contribution from all non-multijet SM backgrounds in the signal region. The estimate of the contribution from multijet events in a given H T bin of the signal region relies on the exponential model R α T (H T ) = Ae −kH T , as described in Section 6. The systematic uncertainties (10-30%) associated with the transfer factors, discussed in Section 5.4, are accommodated in the likelihood function by a nuisance parameter per transfer factor. The measurements of these parameters are assumed to follow a log-normal distribution.
In order to test the compatibility of the observed yields with the expectations from only SM processes, the likelihood function is maximised over all fit parameters. For each of the eight categories of events defined by requirements on n jet and n b , the goodness-of-fit of the SM-only hypothesis is determined by considering simultaneously up to eight bins in H T from the signal region and up to 22 bins from the three control samples. No significant tension is observed in the signal and control regions, which are well described by the SM hypothesis. The p-values obtained are found to be uniformly distributed, with a minimum observed value of 0.1. Table 4 summarises the observed yields and fit results in bins of H T for events in the signal region categorised according to n jet and n b .
Comparisons of the observed yields and the SM expectations in bins of H T for events categorised according to n jet and containing exactly zero, one, or two b-quark jets are shown in Figs. 3, 4, and 5, respectively. Similarly, Fig. 6 shows the H T -binned observed yields and SM expectations for events satisfying n jet ≥ 4 and n b = 3 (left) or n b ≥ 4 (right). For illustration, Figs. 3-6 include the expected yields from various reference models, as defined in Table 1. Figure 7 (left column) shows the observed yields and SM expectations in the H T bins of the µ + jets, µµ + jets, and γ + jets control samples for events satisfying 2 ≤ n jet ≤ 3 and n b = 0. Figure 7 (right column) shows the observed yields and SM expectations in the H T bins of the µ + jets sample for events satisfying n jet ≥ 4 and n b = 2, n b = 3, or n b ≥ 4.
The maximum-likelihood values for the decay constant and normalisation parameters, k and A, of the exponential model for the multijet background are obtained independently for each of the eight event categories. The value of the nuisance parameter k is constrained via a measurement in a multijet-enriched data sideband, as described in Section 6. No constraint is applied to the normalisation term. In the nominal fit, the maximum-likelihood value of the normalisation parameter for each event category is found to be compatible with zero within uncertainties. Furthermore, the expected yields obtained from an alternate fit, in which the normalisation parameters are fixed to zero, agree well with those obtained from the nominal fit.

Interpretation of the results
Limits are set in the parent sparticle and LSP mass parameter space of the simplified models listed in Table 1. The CL S method [53,54] is used to compute the limits, with the one-sided (LHC-style) profile likelihood ratio as the test statistic [55]. The sampling distributions for the test statistic are built by generating pseudo-data from the likelihood function, using the respective maximum-likelihood values of the nuisance parameters under the SM backgroundonly and signal-plus-background hypotheses. Signal contributions in each of the data samples are considered, though the only significant contribution occurs in the signal region and not the control samples. Table 5 specifies the event categories, defined in terms of n jet and n b , used to provide interpretations in the different simplified models. Table 5: A summary of the event categories used to provide an interpretation in the various simplified models considered in this paper.
Event samples for the simplified models are generated at leading order with PYTHIA 6.4 [50]. Inclusive, process-dependent, NLO calculations of SUSY production cross sections, with nextto-leading-logarithmic (NLL) corrections, are obtained with the program PROSPINO [56][57][58][59][60][61]. The samples are generated using the CTEQ6L1 [62] PDFs. The distribution of the number of pp interactions per bunch crossing for the simulated samples matches that observed in data.
Various experimental uncertainties on the expected signal yield are considered for each interpretation. Signal acceptance in the kinematic region defined by 0 < m parent − m LSP < 175 GeV or m parent < 300 GeV is due in part to the presence of initial-state radiation. Given the large associated uncertainties from simulation for this kinematic region, no interpretation is provided. Otherwise, the experimental systematic uncertainties are determined for each point in the mass parameter space of each simplified model. Models are categorised according to the mass splitting between the parent sparticle and the LSP, with those satisfying 175 < m parent − m LSP < 350 GeV deemed to be characterised by a compressed spectrum. For a given category of model, i.e. with a compressed spectrum or otherwise (as defined above), the systematic uncertainties are relatively stable throughout the mass plane, thus a single conservative value is considered for each category.
Estimates of the various systematic uncertainties for models with a compressed spectrum or otherwise are summarised in Tables 6 and 7, respectively. Contributions from the analysis selection are dominated by uncertainties on the PDFs, jet energy scale (JES), and modelling of the efficiency and mistag probability of b-quark jets in simulation. The total systematic uncertainties provided in the tables also account for the uncertainty of 4.4% on the luminosity measurement [13] and contributions from other event selection criteria, such as: the trigger conditions; the removal of events containing isolated muons, electrons, or photons; and filters to suppress classes of rare, pathological events, as described in Section 4.3. Each of these individual contributions is below 4%. The total systematic uncertainty on the expected signal yield for the various simplified models is found to be in the range 12%-23% and is accounted for with a nuisance parameter, the measurement of which is assumed to follow a lognormal distribution. Table 6: Estimates of the dominant systematic uncertainties (%), defined in the text, on the analysis efficiency for various simplified models that are characterised by a small mass splitting (i.e. compressed spectrum) between the parent sparticle and LSP. The totals also reflect contributions from additional systematic uncertainties described in the text. The region m parent − m LSP < 350 GeV is kinematically forbidden for the G3 model. Two sets of excluded regions are provided for the model D1, as shown in Figure 8 (top left). The larger of the two excluded regions is determined assuming an eightfold degeneracy for the masses of the first-and second-generation squarks, q L and q R ( q = u, d, s, and c), and decoupled third-generation squarks and gluinos. The smaller of the two excluded regions assumes the pair production of a single light squark, u L , with the gluino and all other squarks decoupled to high masses. The models D2 and D3 assume the pair production of a single bottom and top squark, respectively. Table 8 lists the expected signal yields and analysis efficiencies in the region H T > 375 GeV for each of the reference models defined in Table 1. The yields and efficiencies are summed over the individual event categories used for each interpretation, as listed in Table 5. The observed and expected upper limits (95% CL) on the cross section are also quoted, which can be compared with the NLO+NLL SUSY production cross section and its theoretical uncertainty.

Model
The estimates of mass limits are determined from the observed exclusion based on the theoretical production cross section, less one-standard-deviation uncertainty. The most stringent mass limit on the parent sparticle, m best parent , is generally obtained at low LSP masses. Generally speaking, the excluded mass range for m parent is bounded from below by the kinematic  Table 8: Summary of expected yields, analysis efficiencies, and upper limits for the reference models defined in Table 1 using the event categories defined in Table 5. The first row specifies the reference model. The second and third rows quote the expected yield and analysis efficiency (with statistical uncertainties) for the region H T > 375 GeV. The fourth row quotes the NLO+NLL SUSY production cross section (with theoretical uncertainty). For the model D1, this cross section assumes an eightfold mass degeneracy. In the case of only a single light squark, the cross section is 25 ± 4 fb. The fifth and sixth rows quote the observed and expected upper limits (95% CL) on the production cross section. region considered for each model, yielding an exclusion that is generally valid for the region m LSP + 175 GeV m parent m best parent . Whether an exclusion can be determined for very small mass splittings, satisfying m parent − m LSP < 175 GeV, requires further detailed studies of the modelling of, for example, initial-state radiation, JES, or the identification of b-quark jets. The upper bound on m parent weakens for increasing values of LSP mass until a value m best LSP is reached, beyond which no exclusion on m parent can be set. Table 9 summarises the most stringent observed and expected mass limits, in terms of m best parent and m best LSP , obtained for the simplified models considered in this paper. The observed exclusion for each simplified model is generally weaker than expected at the level of 1-2 standard deviations. This feature is attributed to the small upward fluctuations in data in either the region H T > 875 GeV for the n b = 0 category or 475 < H T < 675 GeV for the categories of events satisfying 1 ≤ n b ≤ 2. Candidate events in these regions have been examined and do not exhibit any non-physical behaviour. The expected search sensitivity has improved with respect to the analysis based on the √ s = 7 TeV dataset [24] by as much as 225 and 150 GeV for m best parent and m best LSP , respectively.  Figure 9 shows the observed upper limit at 95% CL on the production cross section as a function of the top-squark mass (m t ) for the model D3 when considering different LSP masses in the range 0-150 GeV. No exclusion on possible top-squark masses is observed when considering the theoretical production cross section, less 1σ uncertainty. However, the expected exclusion covers the ranges 300-520, 320-520, and 420-480 GeV for m LSP = 0, 50, and 100 GeV, respectively. No exclusion is expected for the LSP with a mass greater than 100 GeV. The expected reach for the D3 model is summarised in Table 9.

Summary
An inclusive search for supersymmetry with the CMS experiment is reported, based on a data sample of pp collisions collected at √ s = 8 TeV, corresponding to an integrated luminosity of 11.7 ± 0.5 fb −1 . Final states with two or more energetic jets and significant E T / , as expected from the production and decay of massive squarks and gluinos, have been analysed.
The analysis strategy is to maximise the sensitivity of the search to a wide variety of SUSY event topologies arising from squark-squark, squark-gluino, and gluino-gluino production and decay, particularly those with third-generation squark signatures, while still maintaining the inclusive nature of the search. The signal region is binned according to the number of reconstructed jets, the scalar sum of the transverse energy of jets, and the number of jets identified to originate from bottom quarks. The sum of standard model backgrounds per bin has been estimated from a simultaneous binned likelihood fit to event yields in the signal region and 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 set in the SUSY particle mass parameter space of simplified models, with an emphasis on the different production mechanisms of coloured SUSY particles, third-generation squark signatures, and compressed-spectrum scenarios. The results can also be used to perform interpretations in other relevant models, such as the CMSSM.
In the context of simplified models, gluino masses below ∼1 TeV are excluded at the 95% CL under the assumptions that gluinos are produced in pairs and each decays to a quark-antiquark pair and a light LSP via an off-shell squark. The mass limit varies in the range 950-1125 GeV depending on the squark flavour. The most constraining mass limits on the LSP from the decay of a gluino are in the range 325-650 GeV depending on the decay mode. For the direct production of first-and second-generation squark pairs, each of which is assumed to decay to a quark of the same flavour and the LSP, masses below 750 GeV are excluded (95% CL) under the assumption of an eightfold mass-degeneracy. The most constraining mass limit on the LSP is 300 GeV. These limits weaken to 450 and 100 GeV respectively if only a single squark is assumed to be light. For the direct production of bottom squark pairs, each of which is assumed to decay to a bottom quark and the LSP, masses below 600 GeV are excluded. No exclusion is possible for an LSP mass beyond 200 GeV. No exclusion is observed for the direct pair production of top squarks, each of which is assumed to decay to a top quark and the LSP. However, an exclusion is expected for top squark masses as high as ∼500 GeV and an LSP mass as high as 100 GeV. The limits on the LSP masses are also generally valid for compressed-spectrum models with mass splittings between the parent sparticle and LSP as low as ∼200 GeV.
The analysis strategy reported here, in conjunction with the increase in centre-of-mass energy to 8 TeV, has increased the coverage of the SUSY parameter space with respect to previous searches. However, a large range of the SUSY parameter space still remains to be probed by the LHC.