Searches for third-generation squark production in fully hadronic final states in proton-proton collisions at \TeV
Searches for third-generation squarks in fully hadronic final states are presented using data samples corresponding to integrated luminosities of 19.4 or 19.7\fbinv, collected at a centre-of-mass energy of 8\TeVwith the CMS detector at the LHC. Three mutually exclusive searches are presented, each optimized for a different decay topology. They include a multijet search requiring one fully reconstructed top quark, a dijet search requiring one or two jets originating from b quarks, and a monojet search. No excesses above the standard model expectations are seen, and limits are set on top and bottom squark production in the context of simplified models of supersymmetry.
The standard model (SM) of particle physics has proven to be remarkably robust. Nonetheless, the SM has well-known shortcomings, such as an instability in the calculation of the Higgs boson mass known as the fine-tuning (or hierarchy) problem [1, 2, 3, 4, 5]. The discovery of a Higgs boson with a mass of about 125\GeV [6, 7, 8] at the CERN LHC has reinforced the acuteness of this problem. These shortcomings suggest that the SM is merely a low-energy approximation of a deeper, more complete theory. Supersymmetry (SUSY) [9, 10, 11, 12, 13, 14, 15] is a widely considered extension of the SM that introduces an additional symmetry of nature between fermions and bosons. A new supersymmetric particle (sparticle) is proposed for each SM particle, with the same mass and quantum numbers but with a spin that differs by a half-integer unit. For example, squarks are the SUSY partners of quarks. Supersymmetric models contain extended Higgs sectors. The SUSY partners of the Higgs bosons are higgsinos. Neutral (charged) higgsinos mix with the SUSY partners of the neutral (charged) electroweak gauge bosons to form neutralinos \PSGcz(charginos \PSGcpm). Divergent quantum corrections to the Higgs boson mass due to virtual SM particles are cancelled by corresponding contributions from virtual sparticles [16, 17, 18, 19], thus resolving the fine-tuning problem.
The symmetry proposed by SUSY cannot be exact, as no sparticles have yet been observed. However, the stabilising features of SUSY can survive with a modest amount of fine tuning if sparticles are not much heavier than their SM counterparts. For third-generation particles in particular, the mass difference between a particle and its corresponding sparticle should not be too large, in order for SUSY to provide a so-called “natural” solution [20, 21, 22, 23] to the fine-tuning problem. Thus the SUSY partners of top and bottom quarks, the top and bottom squarks \PSQtand \PSQb, respectively, might have masses below or around the TeV scale and be accessible at the LHC. In SUSY models with -parity  conservation, top and bottom squarks can be pair produced, with each top or bottom squark initiating a decay chain in which the end products are SM particles and a stable lightest supersymmetric particle (LSP). In many SUSY scenarios the LSP is the lightest neutralino \PSGczDo, which is weakly interacting and will escape detection, leading to a distinctive experimental signature of large momentum imbalance in the plane perpendicular to the beam axis.
This paper presents three complementary searches for the direct production of either a pair of top squarks () or bottom squarks () decaying to fully hadronic final states with large transverse momentum imbalance. The searches are based on proton-proton collision data collected using the CMS detector at the LHC at a centre-of-mass energy of 8\TeVand correspond to an integrated luminosity of 19.4 or 19.7\fbinvdepending on the study . Each search is separately optimized for different kinematic regimes of top or bottom squark masses, as well as for mass differences between the squark and LSP, where the LSP is taken to be the \PSGczDo. They are: (1) a search for top-squark pair production in multijet events with at least one tagged hadronically decaying top quark (hereafter referred to as the “multijet t-tagged” search), which is sensitive to scenarios with a large mass difference between the top squark and the LSP; (2) a search for dijet events with exactly one or two tagged bottom-quark jets (b jets) possibly accompanied by additional jets radiated in the initial state (hereafter referred to as the “dijet b-tagged” search), which is sensitive to scenarios with large or intermediate mass differences between the bottom squark and the LSP; and (3) a search for events with a single jet (hereafter referred to as the “monojet” search), which is sensitive to scenarios with highly compressed spectra, \ieto scenarios in which the mass difference between the top or bottom squark and the LSP is small. The results from the three searches are combined and interpreted in the context of simplified model spectra (SMS) . Previous searches for top- and bottom-squark pair production at the LHC are presented in Refs. [27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39].
This paper is organised in the following way. Section 0.2 describes the CMS detector, and Section 0.3 discusses event reconstruction algorithms. The simulations of signal and background events are outlined in Section 0.4. A summary of the strategies shared by all three searches, including common event selections and backgrounds, are discussed in Section 0.5. The multijet t-tagged search is presented in Section 0.6, the dijet b-tagged search in Section 0.7, and the monojet search in Section 0.8. Finally, the results are shown in Section 0.9 and interpreted using SMS in Section 0.10, with a summary in Section 0.11. Additional information for model testing can be found in Appendix .12.
0.2 The CMS detector
The central feature of the CMS apparatus is a superconducting solenoid of 6\unitm internal diameter, providing a magnetic field of 3.8\unitT. Within the superconducting solenoid volume are a silicon pixel and strip tracker, a lead tungstate crystal electromagnetic calorimeter (ECAL), and a brass and scintillator hadron calorimeter (HCAL), each composed of a barrel and two endcap sections. Muons are measured in gas-ionization detectors embedded in the steel flux-return yoke outside the solenoid. Extensive forward calorimetry complements the coverage provided by the barrel and endcap detectors.
The polar angle , defined with respect to the anticlockwise-beam direction, the pseudorapidity , defined as , and the azimuthal angle in the plane perpendicular to the beam axis, define the coordinates used to describe position within the detector. The transverse momentum vector \ptvecof a particle is defined as the projection of its four-momentum on to the plane perpendicular to the beams. Its magnitude is referred to as \pt.
The silicon tracker measures charged particles within the pseudorapidity range . Isolated particles of \GeVemitted with have track resolutions of 2.8% in \ptand 10 (30)\mumin the transverse (longitudinal) impact parameter . The ECAL and HCAL measure energy deposits in the pseudorapidity range . Quartz-steel forward calorimeters extend the coverage to . The HCAL, when combined with the ECAL, measures jets with a resolution . Muons are measured in the pseudorapidity range . Matching muons to tracks measured in the silicon tracker results in a relative transverse momentum resolution for muons with of 1.3–2.0% in the barrel and better than 6% in the endcaps. The \ptresolution in the barrel is better than 10% for muons with \ptup to 1\TeV .
The events used in the searches presented here were collected using a two-tier trigger system: a hardware-based level-1 trigger and a software-based high-level trigger. A full description of the CMS detector and its trigger system can be found in Ref. .
0.3 Event reconstruction
Events are reconstructed with the CMS particle-flow algorithm [44, 45]. Using an optimized combination of information from the tracker, the calorimeters, and the muon systems, each particle is identified as a charged hadron, neutral hadron, photon, muon, or electron. Charged hadrons that do not originate from the primary vertex, defined by the pp interaction vertex with the largest sum of charged-track values, are not considered. The remaining particles are clustered into jets using the anti-\ktalgorithm with distance parameter 0.5 . Calorimeter energy deposits corresponding to neutral particles originating from overlapping pp interactions, “pileup”, is subtracted on an event-by-event basis using the jet-area method . Jets are corrected to take into account the detector response as a function of jet \ptand , using factors derived from simulation. The jets must satisfy loose identification criteria that remove calorimeter noise. An additional residual energy correction, derived from dijet and +jets events, is applied to account for differences in the jet energy scales  between simulation and data.
Both the multijet t-tagged and dijet b-tagged analyses employ tagging of b quark jets (b tagging). Utilising the precise inner tracking system of the CMS detector, the combined secondary vertex (CSV) algorithm  uses secondary vertices, track-based lifetime information, and jet kinematics to distinguish between jets from b quarks and those from light quarks or gluons.
In the multijet t-tagged analysis, a jet is tagged as a b quark jet if it satisfies \GeV, , and the medium working point requirements of the algorithm . Averaged over \ptin \ttbarevents, the b quark identification efficiency is 67% for the medium working point, and the probability for a jet originating from a light quark or gluon to be misidentified as a b quark jet is 1.4%. The dijet b-tagged analysis uses the loose and medium working point versions of the algorithm. The b-tagging efficiency is 80–85% (46–74%) for the loose (medium) working point , and the probability for a jet originating from a light quark or gluon to be misidentified as a b quark is 8–12% (1–2%). Values are quoted for jets with \GeVand are dependent on the jet \pt.
Muons are reconstructed by finding compatible track segments in the silicon tracker and the muon detectors . Both the dijet b-tagged and multijet t-tagged analyses require muons to lie within , whereas the monojet analysis uses muons up to . Electron candidates are reconstructed from a cluster of energy deposits in the ECAL that is matched to a track in the silicon tracker . Electron candidates are required to satisfy or , where the intermediate range of is excluded to avoid the transition region between the ECAL barrel and endcap, in which the reconstruction efficiency is difficult to model. Muon and electron candidates are required to originate within 2\unitmm of the beam axis in the transverse plane. In the monojet analysis, hadronically decaying leptons are reconstructed using the “hadron-plus-strips” algorithm , which reconstructs candidates with one or three charged pions and up to two neutral pions.
A relative lepton isolation parameter is defined as the sum of the \ptof all photons and all charged and neutral hadrons, computed in a cone of radius around the lepton direction, divided by the lepton \pt. Values are corrected for the effect of pileup. Lepton candidates with relative isolation values below 0.2 are considered isolated in the monojet and dijet b-tagged analyses.
In the multijet t-tagged analysis, a key ingredient for providing good background rejection and simultaneously preserving good signal selection involves vetoing prompt leptons from or boson decays, while accepting possible secondary leptons from b quark decays. Hence events containing a muon or electron with \GeVare vetoed based on the spatial distribution of particles around the lepton. A directional isolation parameter is defined by considering particles in a region of radius centred on the lepton direction, where is 0.2 for muons and 0.2 (0.3) for electrons with . A sum is performed over the particle transverse momenta multiplied by the square of the angle in the – plane between the particle and the \pt-weighted centroid of all particles contributing to the sum . Leptons from heavy-quark decays usually are closer to hadronic activity in – space than leptons from on-shell or boson decays. The requirements on have been chosen to retain high rejection efficiency, especially for high-\ptleptons, and a small misidentification rate for leptons from b quark decays. This is the first CMS publication to make use of this variable.
The hermetic nature of the CMS detector allows event reconstruction over nearly the full solid angle. Conservation of momentum in the transverse plane can therefore be used to detect a momentum imbalance, which can be associated with particles that exit the detector without interaction. The missing transverse momentum vector \ptvecmissis defined as the projection on the plane perpendicular to the beam axis of the negative vector sum of the momenta of all reconstructed particles in an event. Its magnitude is referred to as . For the monojet analysis, an alternative definition of \ptvecmissis used, , which differs from the nominal definition in that the contribution of muons is excluded. This alternative definition allows the same trigger, for which missing transverse momentum is defined without muons, to be used for both signal and control samples, reducing systematic uncertainties. The alternative definition is also used to evaluate some electroweak backgrounds for the multijet t-tagged and dijet b-tagged analyses, as described below.
0.4 Simulation of signal and background event samples
Monte Carlo (MC) simulations of signal and background events are used to optimize selection criteria, determine signal efficiencies, and develop background estimation techniques.
Within the context of natural SUSY, several SMS scenarios are examined. They are based on the pair production of top or bottom squarks followed by the decay of the top or bottom squarks according to , with , , and , where \PSGcpmDois the lightest chargino. The Feynman diagrams for these processes are shown in Fig. 1. Simulated samples of signal events are generated with the \MADGRAPH22.214.171.124  event generator, with up to two additional partons incorporated at the matrix element level. All SUSY particles other than those included in the SMS scenario under consideration are assumed to be too heavy to participate in the interaction.
SM events are simulated using a number of MC event generators. Top-antitop quark pair production (\ttbar), \PW/\Z+jets, , , , and samples are produced using the \MADGRAPH5 event generator with CTEQ6L  parton distribution functions (PDFs). Single top quark events are generated with the \POWHEG  program using the CT10  and CTEQ66  PDFs. Multijet events from QCD processes and events with WW, WZ and ZZ (diboson) production are simulated with the \PYTHIA6.4.24  program using the CTEQ6L PDFs.
For both the signal and SM simulated samples, the parton shower, hadronization, and multiple-parton interactions are described using \PYTHIA. Decays of leptons are handled by the \TAUOLA27.121.5 package . The generated events are interfaced to the CMS fast detector simulation  for the signal samples and to a \GEANTfour-based  detector simulation for the SM background samples.
0.5 Search strategy
The analyses presented here are designed to be efficient for possible signals, while maintaining manageable background levels. All three searches require at least one high-\ptjet and a large value of . Background from QCD multijet events is reduced by a minimum angle between the directions of the \ptvecmissvector and highest \ptjet(s). Electroweak backgrounds are reduced by vetoing events with leptons. Use of b tagging and kinematic variables further distinguishes signal from background.
The sources of SM background, and the background evaluation procedures, are also similar in the three searches. Events with a boson that decays to neutrinos, denoted +jets, contain genuine and constitute a significant background. This background is estimated using dimuon control samples, exploiting the similar kinematics of and events as well as the known branching fractions. In regions where \ttbarcontamination is small, events with can similarly be used to estimate the +jets background. Another significant source of background is from events when the boson decays leptonically, denoted +jets events. Here, the lepton (electrons and muons, including those from leptonically decaying leptons) fails the lepton veto and hence is “lost”, i.e. it is not isolated, not identified, or outside of the acceptance of the analysis. Hadronically decaying leptons () from boson decay in \ttbarand events form another significant background source. Both the lost-lepton and backgrounds are evaluated using single-muon control samples. Dijet and multijet backgrounds are reduced using topological selections, with the remaining contributions estimated using data control regions enhanced in QCD events. Very small backgrounds from processes such as diboson, , , and single top quark are estimated from simulation. The data control regions used in the estimates of the SM backgrounds are defined in such a manner to minimize the contributions of signal events, and thus possible signal event contributions to control regions are ignored.
0.6 Search for top-squark pair production using top-quark tagging
This search for pairs of hadronically decaying top quarks with large in the final state is motivated by the scenario of top-squark pair production, assuming that the mass difference between the top squark and the stable LSP is larger than the mass of the top quark, . The decay channel is therefore kinematically available, allowing a search for top squarks through top quark tagging, which provides an important discriminant against the multijet background. If \PSGcpmDostates exist with a mass between the top squark and the LSP masses, the top squark can also decay via (plus its charge conjugate), yielding a different event signature since no top quark is produced. By requiring just one fully reconstructed top quark, the search maintains sensitivity to as well as decays.
0.6.1 Event selection
The event sample used for this analysis is collected by triggering on events with \GeV, where is reconstructed using the particle-flow algorithm, and at least two central () jets with \GeV. This trigger is efficient as measured in data once the analysis requirements described below have been applied. The selected events are required to have: (i) no identified electrons or muons with \GeV that are isolated according to the directional isolation parameter described in Section 0.3; (ii) at least five jets with \GeVand , of which the two highest \ptjets must have \GeVand the next two highest \ptjets \GeV; (iii) at least one b-tagged jet, ; and (iv) azimuthal angle between the directions of the three highest \ptjets and the \ptvecmissvector larger than 0.5, 0.5, and 0.3, respectively, with . The electron and muon vetoes minimize backgrounds from SM \ttbarand \PW+jets production, where the \PW boson decays into a neutrino and a lepton. Events containing a hadronically decaying lepton are not explicitly rejected. The jet multiplicity and b-tagging requirements help to select signal events, since the SUSY signatures of interest tend to include multiple jets in the central range, high-\ptleading jets and b jets. The requirement strongly suppresses the background from QCD multijet events, which mostly arises from the mismeasurement of jet \pt, leading to large \ptvecmissaligned along a jet axis. Events that satisfy the above requirements are denoted the “preselection” sample.
Reconstruction of hadronically decaying top quarks is performed as suggested in Refs. [63, 64, 65]. To maximize signal acceptance, one “fully reconstructed” and one “partially reconstructed” top quark are required. The collection of five or more jets in the preselection sample is divided into all possible sets of three jets and a remnant, where the remnant must contain at least one b-tagged jet. The fully reconstructed top quark is one of the three-jet (trijet) combinations. The partially reconstructed top quark is then built from the remnant using the b-tagged jet as a seed. If the remnant contains multiple b-tagged jets, the one with highest \ptis used as the seed. Once events with two candidate top quarks are identified, they are used to form additional kinematical variables that distinguish between signal and the remaining SM background, which arises primarily from \ttbarproduction.
Top quark reconstruction
To be considered as a fully reconstructed top quark, the trijet system must satisfy the following requirements. (i) Each jet must lie within a cone in () space of radius 1.5 centred on the momentum direction formed by the trijet combination. The radius requirement implies a moderate Lorentz boost of the top quark as expected for the large region targeted in this search. (ii) The trijet system mass () must be within the range 80-270\GeV. (iii) The trijet system must satisfy one of the three following criteria:
Here, , , and are the dijet masses, where the jet indices 1, 2, and 3 are \ptordered. The numerical constants have values , , \GeV, and \GeV .
The top quark tagging (t tagging) conditions of (a), (b), or (c) can be reduced (under certain approximations detailed in Ref.  ) to the requirement that , , or , respectively, be consistent with the ratio. The other conditions are motivated by the Lorentz structure of the tW coupling and suppress contributions from light-quark and gluon jets . These t tagging conditions are illustrated in Fig. 2 for simulated SM \ttbar(left) and QCD (right) events. The lower box defines the region dictated by the criterion (a), with the central dashed horizontal line representing the ratio . Similarly, the curved regions defined by criteria (b) and (c) are also shown, where the central dashed line indicates where is equal to for region (b), and where is equal to for region (c). The requirement that events lie within the boundaries defined by (a), (b), or (c) is seen to be effective at selecting the SM \ttbarevents, which are very similar to signal events due to similar and ratios, while rejecting the bulk of the multijet background. If multiple trijet combinations satisfy these criteria, the triplet with mass closest to the top quark mass is selected. The four-momentum of the selected trijet system, , is used in the subsequent calculation of kinematical variables that refine the event selection, described below.
The partial reconstruction of a second top quark is attempted in the remnant system, denoted R-sys. The four-momentum of the collective decay products in R-sys is denoted and is constructed from either 3, 2, or 1 jet(s) in R-sys. If R-sys has 3 jets, all possible trijet combinations containing the b-tagged jet are considered. To retain maximum signal acceptance, the full reconstruction criteria of requirements (a), (b) and (c) are not used. Instead we merely select the trijet system with mass closest to that of the top quark. In addition, to reduce the misconstruction of top quark candidates, requirements are placed on the hadronic decay of the \PW boson candidate in the trijet system: excluding the b-tagged jet, the remaining pair of jets is required to have a dijet mass between 50 and 120\GeV. If this condition is satisfied, the four-momentum of the trijet system defines . Otherwise the trijet system is rejected and we examine 2-jet combinations involving the b-tagged jet. In the latter case, the separation between the b-tagged jet and the other jet is required to satisfy and the dijet mass must be less than the top quark mass. If multiple jet pairs satisfy these requirements, the pair with smallest is selected and the four-momentum of the pair defines . If no jet pair satisfies the requirements, the b-tagged jet is selected as the complete remnant system, and its four-momentum defines .
After requiring one fully reconstructed and one partially reconstructed top quark, kinematic information is used to distinguish between signal and SM contributions. The [67, 68] variable, an extension of the transverse mass used for the W boson mass determination , is sensitive to the pair production of heavy particles with decay products that include undetected particles like neutrinos or the \PSGczDo. The variable is constructed using , , and the \ptvecmissvectors in an event, assuming the undetected particles to be massless. The top-left plot in Fig. 3 shows a comparison of the shapes of the two distributions of simulated signal and SM \ttbarevents after applying the preselection criteria and requiring \GeV. The results for signal events are shown for various mass hypotheses for the top squark and LSP. For the \ttbarbackground, the distribution peaks around the top quark mass and decreases relatively quickly for larger values. For the signal, the distribution peaks at higher values. As one of the top quarks is only partially reconstructed, the kinematic endpoint of is only approximately reconstructed. To reduce the SM \ttbarbackground while maintaining good signal efficiency for a range of sparticle mass hypotheses, we require \GeV. The top-right plot in Fig. 3 shows the distribution in the same conditions.
The variable , defined using the \ptvecmissand the fully reconstructed trijet system of the identified top quark,
is also used to distinguish between signal and SM \ttbarevents, where . Here, is the magnitude of in the transverse plane and is the azimuthal angle between \ptvecmissand . The variable is similarly defined using Eq. (1), by replacing the “3-jet” variables with those of the partial top quark decay products in R-sys. The bottom row in Fig. 3 shows distributions of versus for SM \ttbarsimulated events (left) and for simulated events from a typical signal (right). All events are required to satisfy the preselection requirements and to have . For signal events, the requirement typically forces the two top quarks to lie in the hemisphere opposite to \ptvecmiss. This leads to larger values of and due to the large azimuthal angle differences involved. In contrast, for SM \ttbarevents, \ptvecmisstypically lies close to one of the two top quarks, and thus either or tends to have a smaller value. The resulting correlations can be used to further reduce the SM \ttbarbackground. Based on simulation, a simple linear requirement \GeVis imposed [see the diagonal lines in Fig. 3 (bottom)]. This requirement is found to be more effective than simple restrictions on and separately.
Four exclusive search regions are selected, defined by \GeVand with exactly one or at least two b-tagged jets. The requirement increases the sensitivity for high-mass top squark production. We further define a “baseline” selection \GeVand that encompasses all exclusive regions. Yields for different processes in each of the search regions are shown in Table 0.6.1.
0.6.2 Background predictions
The background is evaluated using a combination of control samples in data and results from MC simulation, following procedures established in Refs. [70, 71]. The SM backgrounds from \ttbar, +jets, and QCD multijet production are estimated using data control regions. The background from +jets production is estimated using simulated events that are scaled to match the data in control regions. The SM backgrounds from rare processes, such as , and production with at least one or decay, are small and estimated directly from simulation.
The background from SM events with a lepton is estimated from a data control sample selected using a trigger requiring a muon with , and at least three jets, each with . To define the control sample, we require the muon to be isolated (as defined in Section 0.3) and to have and . To select events with a candidate, the transverse mass is required to be less than 100\GeV, where is the azimuthal angle between the and the \ptvecmissdirections. Since the +jets and +jets events arise from the same physics processes, the hadronic component of the two samples is the same except for the response of the detector to the muon or lepton. To account for this difference, the muon in the data control sample is replaced by a simulated lepton (a “ jet”). The resulting is simulated using a response function obtained from MC simulated events. The jet in the MC simulated event is reconstructed and matched to the generated lepton, in bins of the generated lepton \pt. Corrections are applied to account for the trigger efficiency, acceptance and efficiency of the selection, requirement efficiency, contamination from decays, and the ratio of branching fractions . The , \ptvecmiss, , , and results for each event in the +jets data control sample are then recalculated with this simulated jet, and the search region selection criteria are applied to predict the background. The background estimation method is validated by applying it to simulated \ttbarand \PW+jets samples. For the and variables, the predicted distributions reproduce the expected distributions within statistical uncertainties.
Due to the multiple sampling of the response template, the uncertainty in the prediction is evaluated with a set of pseudo-experiments using a bootstrap technique . The main systematic uncertainties in the background estimation arise from the statistical precision of the validation method (6–21%), the acceptance (3–4%), and the -jet response function (2–3%) . An additional uncertainty of 3–14% is assigned to the background prediction to account for differences between the simulation and data for the efficiency of the requirement, which arise as a consequence of finite resolution in and because of uncertainties in the fraction of dileptonic \ttbarevents.
The lost-lepton background arises from SM \ttbarand \PW+jets events. It is estimated using a +jets control sample selected with the same trigger and selection criteria as those used for the search, except requiring (rather than vetoing) exactly one well reconstructed, isolated muon with \GeV. As in the estimation of the background, only events with \GeVare considered. Leptons lost due to non-identification and non-isolation are treated separately. The reconstruction and isolation efficiencies of the electrons and muons respectively, and , are taken from \ttbarsimulation in the lepton \ptbins after the baseline selection. To estimate the number of events with unidentified leptons in the search regions, the ratio is applied to the number of events in the control sample; similarly, the number of events with non-isolated leptons is estimated using . The acceptance and efficiencies are validated with “tag-and-probe” studies of () events in data and simulation . The method is validated by predicting the lost-lepton background using a single-muon sample from simulated \ttbarand events. The predicted distributions and the true distributions (taken directly from the simulation) agree within the uncertainties.
The dominant uncertainties in the lost-lepton background prediction arise from the differences in lepton reconstruction and isolation efficiencies between data and MC simulation. The uncertainties due to lepton reconstruction efficiency are determined by comparing tag-and-probe efficiencies in events at the \Zboson mass peak in data and simulation. For isolation uncertainties, the isolation variables in the simulation are scaled to match the distribution from the data, and the resulting differences in predictions are taken as a systematic uncertainty. Variations of the PDFs following the recommendation of Refs. [74, 75] change the muon acceptance, but lead to less than 3% uncertainty in the final prediction. An additional uncertainty of 3% is assigned to account for possible differences between data and simulation for the requirement, evaluated in the same manner as for the background.
The +jets background is estimated from +jets simulation, with a normalization that is adjusted to account for differences with respect to data using a scale factor determined from a dimuon control sample. The dimuon control sample is selected using the preselection criteria of Section 0.6.1, except that the lepton veto is removed and instead, a pair is required to be present. The and must satisfy \GeV, , a relative isolation parameter 0.2 (as defined in Section 0.3), and the dimuon mass must lie in the boson mass range 71–111\GeV. To mimic the effect of neutrinos, is used. The dimuon control sample includes events from \ttbarand production, which must be subtracted. The \ttbarcontribution is evaluated using simulation, with a normalization that is validated using a single-lepton (electron or muon) control sample with lepton \GeV. In the single-lepton control sample, we also validate the normalization of the simulation after requiring either or . The normalization in the single-muon control sample is found in all cases to be consistent with unity. A statistical uncertainty in this unit normalization (6–8%) is propagated as a systematic uncertainty in the normalization of the \ttbarcontribution to the dimuon control sample. The contribution to the dimuon control sample is estimated directly from simulation. The scale factor is defined by the ratio of data to MC events in the dimuon control sample, after subtraction of the \ttbarand components. The scale factor is found to be statistically consistent with unity for events with exactly zero b-tagged jets. Events with one b-tagged jet are found to have a scaling factor of (stat). In events with two or more b-tagged jets, the scaling factor is found to be (stat).
Systematic uncertainties in include uncertainties in the normalization and subsequent removal of the \ttbarand processes (1–5%), uncertainties in the simulation to account for muon acceptance (10%), trigger efficiency uncertainties (1%), and data-versus-simulation shape disagreements. The shape disagreements are divided into an overall normalization uncertainty (26–33%) to account for discrepancies in the normalization due to the remaining event selection requirements, and a residual shape uncertainty (up to 80%) which accounts for potential normalization or shape discrepancies in the tails of the analysis variables. The residual shape uncertainty is taken from the envelope of a first-order polynomial fit to the data/MC ratio of the analysis variables. An asymmetric systematic uncertainty is assigned to account for the difference between this fit envelope and the overall normalization uncertainty.
The QCD multijet background is expected to be small due to the and requirements. This background is estimated by measuring the number of QCD multijet events in a data control region and scaling the yield by a factor , which translates the yield to the search region. The control region is identical to the search region except that one of the three highest \ptjets must fail the respective requirement specified in Section 0.6.1. The factor is defined as , where is the ratio of the number of measured QCD multijet events found with the standard and inverted requirements in a sideband \GeV, and is a MC-derived extrapolation factor that translates to the search region . The analysis requires a reconstructed top quark, at least one b-tagged jet, and large , so the sideband and inverted control regions are dominated by \ttbar, +jets, and \PW+jets events. To determine the number of QCD multijet events in the sideband and control regions, the number of events observed in data is corrected for non-QCD contributions using the method described above for the \ttbarcontribution to the dimuon control sample in the +jets background estimate. Using simulation, the ratio of events in the standard and inverted regions is determined as a function of . The results are fit with a first-order polynomial. The factor, whose value is defined by the slope of this polynomial, is consistent with zero.
The statistical uncertainty from simulation, the jet energy scale uncertainty, and jet energy resolution uncertainty are combined to define a systematic uncertainty in .
The individual contributions to the background, evaluated as described above, are listed in Table 0.6.2 for each of the four search regions. Both statistical and systematic uncertainties are indicated. For the QCD multijet background, the predicted event yields for are small, around 0.10 events. The corresponding total uncertainties of around 0.45 events are much larger, with about equal contributions from statistical and systematic terms, and so we merely quote these latter results as one standard deviation upper limits on the background estimates.
0.7 Search for bottom-squark pair production using bottom-quark tagging
We next describe the dijet b-tagged analysis. This analysis requires large and one or two jets identified as originating from bottom quarks. The possible presence of a hard light-flavour third jet, arising from initial-state radiation (ISR), is incorporated. The search is motivated by the possibility of bottom-squark pair production, where each bottom squark decays directly to the \PSGczDoLSP with the emission of a bottom quark, . The signal production rate depends on the bottom squark mass, while the transverse momenta and hence the signal acceptance of the search depend on the mass difference .
0.7.1 Event selection
The data used in the dijet b-tagged search are collected using the same trigger described in Section 0.6.1 for the multijet t-tagged search. The trigger efficiency is measured to be larger than 95% after application of the selection criteria described below, as measured in data. A set of loose selection criteria are applied to define a baseline data set that is used in addition as a validation sample to compare data and simulation for various kinematic quantities. Exactly two central jets are required with \GeVand , and events are vetoed if they have an additional jet with 50\GeVand . One or both of the leading jets are required to be tagged as originating from a b quark, using the medium CSV algorithm working point. Events containing an isolated electron, muon, or track (representing single-prong -lepton decays or unidentified electrons or muons) with \GeVare rejected to suppress background processes such as \ttbar and +jets production. In addition, the scalar sum \HT of the \ptvalues of the two highest-\ptjets ( and , with ) is required to be more than 250\GeV, and is required to be larger than 175\GeV. To reject QCD dijet events, we require radians. To further suppress the SM background from \ttbar and +jets events, the transverse mass defined by is required to be larger than 200\GeV.
Events are characterized using the boost-corrected contransverse mass [76, 77], which for processes involving two identical decays of heavy particles such as , is defined as . For signal events, the distribution is characterized by an endpoint at .
To obtain sensitivity to different mass hypotheses, the search is conducted in four regions of : , , , or \GeV. For each region, we require either or , for a total of eight exclusive search regions.
For , the \ptvalues of jets from the squark decay become too small to efficiently satisfy the selection requirements. However, events containing a high- jet from ISR can provide a transverse boost to the recoiling system, enabling such events to satisfy the trigger and selection conditions. Additional search regions, hereafter denoted “ISR” search regions, are therefore considered by modifying the baseline selection requirements to allow an additional third jet from ISR: exactly three jets with \pt\GeVand are then required, where the two highest \ptjets must have and the highest \ptjet is required not to be b-tagged using the CSV loose definition. At least one of the two other jets must be b-tagged according to the medium CSV working point, and the events are classified according to whether one or both of these jets are so tagged, defining two ISR search regions. As in the nominal dijet case, events are rejected if they contain isolated leptons or tracks, or if . An additional requirement is , where is the modulus of the vector sum over the transverse momenta of all jets that are not b-tagged. This requirement increases the probability of selecting events with hard ISR jets and is expected to be reasonably efficient for signal processes, as shown for two representative mass hypotheses in Fig. 4. In addition, events must satisfy . To reduce the multijet background, we require radians, where . Finally, no requirement is placed on for the two ISR search regions.
For purposes of illustration, the background estimates predicted by simulation for the 10 search regions are listed in Table 0.7.1. The contribution from QCD multijet production to the search regions is expected to be negligible, so only the upper limits on this background contribution are quoted.
0.7.2 Background predictions
As compared to the multijet t-tagged search, due to jet multiplicity and lepton veto requirements including an isolated track veto, backgrounds involving top quarks are significantly reduced. Instead, in all 10 search regions the dominant background is from +jets events, followed in importance by contributions from W+jets and \ttbar processes. The SM background due to these processes, as well as the contribution from single-top quark production, are determined using data with assistance from simulation. From studies with simulation and data control samples, the contribution of QCD multijet events is expected to be negligible. The contribution of diboson and events in the search regions is less than and is estimated from simulation assuming a 50% systematic uncertainty.
For nine of the search regions, the eight search regions and the ISR search region with , the +jets background is evaluated using a control sample enriched in +jets events as they have similar kinematic properties. For this control sample, which is selected using an isolated muon trigger, the muon is required to have \GeVand to ensure a trigger efficiency near unity. To exclude Drell–Yan processes, an event is vetoed if it contains an additional muon candidate that in combination with the required muon forms a system having invariant mass within 25\GeVof the mass of the \Z boson. To reject muons from decays-in-flight and from semileptonic decays within heavy-flavour jets, the selected muon must be separated by from all jets. The remaining events are accepted and classified using the same criteria that define each of the nine search regions, except that a b-tag veto (using the loose CSV working point) is applied, to minimize the contribution of \ttbar or single top quark processes. The muon \ptvecis removed from the event to mimic the signature of neutrinos from decays of the \Z boson. All kinematic variables are modified accordingly, where is used. Selection thresholds for the resulting , , and variables are the same as those used to define the search regions. In the case of the doubly b-tagged ISR search region, the requirement (which, in this case, is effectively a requirement that the leading jet \ptbe larger than 250\GeV) is common to both the search region and the control sample. The muon selection, in conjunction with the restrictions on and , ensures that the contributions of QCD multijet events are negligible. The requirement thus has minimal impact and is not implemented for the control sample selection. The estimated number of +jets background events is:
where is the ratio of the number of + b jets events in the search region to the total number of events in the control sample, taken from simulation and determined separately for each search region defined by either and (in the case of the eight search regions) or by and (in the case of the doubly b-tagged ISR search region). The term represents the number of events observed in data, in each control region. The number of simulated events in the control sample is corrected for differences between simulation and data in the muon isolation and identification efficiencies as a function of muon \pt, muon , and trigger efficiency.
The +jets control sample described above, when used to evaluate the +jets background in the ISR search region, overlaps with the +jets control sample used to evaluate the +jets background in the ISR search region. Therefore, an alternative data control sample of +jets events is used to evaluate this background in the ISR region to provide sufficient discrimination between control regions. Using the same single-muon triggered control sample, we require the identical selection requirements as for the singly b-tagged ISR search region, except that we demand two opposite-sign, well-identified, isolated central () muons with \GeVand \GeV, respectively, that have an invariant dimuon mass between 76 and 106\GeV. One b-tagged jet is required using the medium CSV definition. In an analogous way to Eq. (2), the number of +jets events is estimated by applying muon and trigger efficiencies, and by scaling the observed number of events in the control region by the factor , which is the ratio from simulation of the number of events in the search region to the total number of events in the control region.
Tests of the method are performed with simulation, treating MC events as data and comparing the predicted number of background events with the true number. Systematic uncertainties are assigned based on the level of agreement: 2–13% for the search regions and 8–30% for the search regions, where the uncertainties are dominated by the statistical precision available. To determine a systematic uncertainty in the number of non-+jets events in the single-muon control sample, the production cross sections of Drell–Yan, diboson, \ttbar, and single-top simulation samples are varied up and down by 50%; less than 10% variation is observed for one or two b jets, across all search regions. The sensitivity of in both the +jets and +jets enriched control samples to muon isolation and identification is also studied. Varying these muon criteria within their uncertainties, and taking the deviations from the central values in each search bin, systematic uncertainties of 3–10% for and 5–10% for are assigned for both the and ISR search regions. Another source of systematic uncertainty in the ratio can arise from differences between data and simulation in the production of Z bosons in association with one or two b jets. The data are observed to agree with the simulation to better than about 5% for events having at least one b jet and covering values up to 250\GeV; we thus apply a 5% systematic uncertainty for all and ISR search regions. Other theoretical systematic uncertainties largely cancel in the ratio of cross sections but are nevertheless considered. Higher-order corrections from QCD are expected to be less than 5%, and the uncertainty from the choice of the PDFs is negligible as higher-order electroweak corrections are similar for W and Z boson production and largely cancel in the cross section ratios .
+jets, \ttbar, and single-top processes make up the lost-lepton background, as defined in Section 0.5. This lost-lepton background is evaluated together with the background due to events via control samples defined by the same dijet-with- trigger used to define the 10 search regions. The event selection criteria for each control region are identical to those used to define the respective search region, except for the following three conditions. First, a single muon is required (rather than vetoed) using tight muon identification criteria. Second, in the cases of the eight search regions, the requirement on is removed. Third, in all 10 control regions, exactly one or exactly two jets must be b-tagged using the loose CSV working point. The prediction in each search region for the number of lost-lepton and background events due to \PW+jets, \ttbar, and single-top processes is given by:
where the factor (determined from simulation) is the ratio of the number of \PW+jets, \ttbar, and single-top events in a particular search region to the number of \PW+jets, \ttbar, single-top, diboson, and Drell–Yan events in the corresponding control region; finally, represents the number of events observed in data for each control region.
The data and simulation samples as well as the control and search regions are all defined to be kinematically similar, so most of the uncertainties due to mismodelling of event kinematics or instrumental effects are expected to largely cancel. However, the relative \ttbar and \PW+jets contribution depends on the b jet multiplicity, which can be different between a search region and its corresponding control region. The accuracies of the factors are tested in data using two independent single-muon triggered samples containing exactly one b jet (expected to contain roughly equal \ttbar and \PW+jets contribution) and exactly two b jets (expected to have a dominant \ttbar contribution). A related source of uncertainty arises from possible differences in the modelling of lepton isolation and the isolated track veto between data and simulation. To probe this effect, the numbers of events with exactly one muon are predicted starting from a control sample with an isolated track and no isolated muon or electron using a transfer factor derived from MC. The average weighted uncertainty of the two studies results in 4–20% differences in the predicted background in various search regions. Statistical uncertainties in the transfer factors, due to the finite size of simulation samples, result in 2–16% and 10–80% uncertainties in the predicted backgrounds, for search regions with one and two b jets, respectively. Uncertainties related to the efficiency of the CSV algorithm to identify b jets result in 2–20% uncertainties in the final background predictions. And finally, uncertainties in the background prediction due to the contributions of dibosons and other rare processes, taken from simulation with 50% uncertainty, are less than 2% across all search regions. The predicted numbers of \ttbar, single-top, and +jets events in the various search regions are listed in Table 0.7.2, along with the statistical and total systematic uncertainties.
Background yields from QCD multijet processes are expected to be less than a percent of the total across all search bins. An estimate of the contribution from the QCD background is made by measuring the number of multijet events in a QCD enriched control region, and scaling this number by a transfer factor. The control regions are identical to the search regions except that the requirement is inverted (for the dijet search regions), and is inverted (for the ISR search regions). In the case of the dijet searches, the transfer factor is taken from a zero b-jet sideband. In the case of the ISR searches, the transfer factor is taken from a sideband defined by .
From studies from simulation, QCD events in the region with the standard requirement survive only because of mismeasurement, where under-measurement of one of the two leading jets results in it being reconstructed as the third jet, where the third leading jet of the event must have \GeV. This behaviour is observed to have no correlation with the b quark content of events. A dijet sideband region with zero b jets is therefore used to estimate the number of QCD events in the search regions. This dijet sideband is divided into two regions: a QCD subdominant sideband region for which together with to enrich the QCD content, and a QCD dominant sideband region defined by . In the QCD subdominant sideband region, the contribution from non-QCD processes (\Z+jets, \ttbar, and \PW+jets events) is significant and is subtracted (via simulation normalized to data) from the observed numbers of events. Contributions from non-QCD processes in the QCD dominant sideband region are negligible. The QCD transfer factors, characterized in bins of and for the eight dijet searches, are then defined as the ratio of the number of multijet events between these two sideband regions.
Using a method similar to the QCD background determination in the multijet t-tagged search, described in Section 0.6.2, the ISR sideband of is divided into two regions: a regular sideband region for which , and an inverted sideband region for which . While QCD processes dominate the inverted sideband region (due to the requirement), non-QCD processes dominate the regular sideband region (due to the large conditions). Using simulation, \Z+jets, \ttbar, and \PW+jets processes are subtracted from the data yields for both sideband regions. The QCD transfer factors are then defined by the ratio of the remaining data yield in the regular sideband region to the remaining data yield in the inverted sideband region. Due to possible correlations between and , the transfer factors are parametrized as a linear function of using simulation. The transfer factor is then extrapolated from the value obtained in the sideband to the value at the average expected from QCD processes in the ISR search regions.
The systematic uncertainty in the QCD background prediction comes from (i) the limited number of observed events in the data control samples, as well as (ii) the limited number of simulated non-QCD events that are subtracted from the sideband regions used to determine the transfer factors. For the ISR search regions, uncertainties associated with the determination of the linear parametrization of the transfer factor are propagated as an additional source of systematic uncertainty in the QCD background prediction.
The background yields using the methods outlined above are summarized in Table 0.7.2.
0.8 Search for top- and bottom-squark pair production in compressed spectrum scenarios
We next describe the monojet search. Given the lack of observation of a SUSY signature in more conventional searches, it is important to search for SUSY with compressed mass spectra, i.e., SUSY scenarios in which the parent sparticles are close in mass to the daughter sparticles. Small mass splittings or between the top or bottom squark and the LSP leave little visible energy in the detector, making signal events difficult to distinguish from SM background. However, events with an energetic ISR jet recoiling against the \ptvecmissvector from the LSP can provide a clear signal for compressed events. We thus perform a search for events with a single jet and significant .
For , the dominant \PSQtdecay mode is the flavour changing neutral-current process . In the case of the , the kinematically similar decay dominates for compressed scenarios, so the monojet topology is used to search for both top and bottom squarks. The search represents an optimization of the studies presented in Refs. [79, 80, 81]. Relative to these previous studies, we increase the threshold on , and define search regions using the \ptof the highest \ptjet rather than .
0.8.1 Event selection
Data used in the analysis are selected by a combination of two triggers. The first trigger requires \GeV, where is calculated using calorimetric information only. The second trigger requires a jet to satisfy \GeV, , and to have less than 95 of the jet momentum carried by neutral hadrons. In addition, the second trigger requires \GeV, where is calculated using the particle-flow algorithm. Selection criteria of \GeV, and a leading jet (which has the highest momentum of all jets in the event and is denoted ) with \GeVand , ensure a fully efficient trigger. To suppress the instrumental and beam-related backgrounds, and to remove noisy events and misidentified high-\ptelectrons and photons, events are rejected based on the properties of : if less than 20% of its energy is carried by charged hadrons, or if more than 70% of its energy is carried by either neutral hadrons or photons, the event is rejected.
Although event selection is based upon a single high-momentum jet, signal acceptance is increased by accepting events in which there is a second jet originating from ISR. In addition, the signal also has soft final-state jets produced by the charm or bottom quarks originating from the sparticle decays. Ideally, these soft jets should not be taken into account in the jet counting. To suppress them a \ptthreshold is introduced for the jet counting. Figure 5 shows the \ptdistribution of charm quarks, taken from simulation, for a few representative mass hypotheses in the process . Placing the jet counting threshold at 60\GeVfor jets with provides a compromise between a high threshold to reject soft jets and a low threshold to reject QCD multijet events. Using this threshold condition, events with up to two jets are accepted. To suppress the QCD dijet background, is required to be less than 2.5. To reduce electroweak and top backgrounds, events with electrons satisfying \GeVand , or muons reconstructed with \GeVand , are rejected. Events with a well-identified lepton with \GeVand are removed. The analysis is performed in search regions that reflect the hardness of the radiated jet in an event, in seven inclusive regions of leading jet \pt: 300, 350, 400, 450, 500, and 550\GeV.
Following the above selection criteria, expected event yields from various SM processes, as predicted by simulation in each of the search regions, are shown in Table 0.8.1.