Search for new physics in the multijet and missing transverse momentum final state in proton-proton collisions at sqrt(s) = 8 TeV

A search for new physics is performed in multijet events with large missing transverse momentum produced in proton-proton collisions at sqrt(s) = 8 TeV using a data sample corresponding to an integrated luminosity of 19.5 inverse femtobarns collected with the CMS detector at the LHC. The data sample is divided into three jet multiplicity categories (3-5, 6-7, and 8 or more jets), and studied further in bins of two variables: the scalar sum of jet transverse momenta and the missing transverse momentum. The observed numbers of events in various categories are consistent with backgrounds expected from standard model processes. Exclusion limits are presented for several simplified supersymmetric models of squark or gluino pair production.


Introduction
The standard model of particle physics (SM) successfully describes a wide variety of observations in high energy physics. The recent discovery of a new scalar boson with a mass of about 125 GeV [1][2][3] at the CERN Large Hadron Collider (LHC) marks another success for the SM, as its properties measured so far are consistent with those of the long-sought Higgs boson. However, its mass is predicted to be unstable against quadratically divergent quantum-loop corrections, which suggests the presence of physics beyond the SM. Supersymmetry (SUSY) is a well-explored extension that addresses various shortcomings of the SM. SUSY postulates a new symmetry, relating fermionic and bosonic degrees of freedom, and introduces a superpartner for each SM particle. Radiative corrections due to SUSY particles can compensate the contribution of the SM particles and thereby stabilize the mass of the Higgs boson. In R-parityconserving models [4], SUSY particles are produced in pairs, and the lightest SUSY particle (LSP) is stable. If weakly interacting and neutral, the LSP is a potential dark matter candidate.
This paper reports an inclusive search for physics beyond the SM in multijet events with large missing transverse momentum produced in pp collisions at a centre-of-mass energy √ s = 8 TeV at the LHC. The data sample used corresponds to an integrated luminosity of 19.5 fb −1 collected by the Compact Muon Solenoid (CMS) experiment [5]. This final state is motivated by many extensions of the SM, for example those given in Refs. [6][7][8]. At the LHC, both the CMS and ATLAS collaborations have performed SUSY searches in all-hadronic final states [9][10][11][12][13][14][15][16][17]. For all these searches, the observed numbers of events were consistent with the expected SM background, and exclusion limits were set in the context of the constrained minimal supersymmetric extension of the standard model (CMSSM) [18][19][20] and various simplified models [21,22]. Contrary to the CMSSM case, the masses of particles are free parameters in simplified models, thus allowing a generic study of the parameter space of SUSY and SUSY-like theories. Simplified models of squark and gluino pair production are used to interpret the search results in this paper.
This analysis follows previous inclusive searches [9, 10] that require at least three jets in the final state. These searches are most sensitive to the hypothetical production of pairs of squarks and gluinos, where the squarks (gluinos) each decay to one (two) jets and an undetected LSP. We extend the analyses of Refs. [9, 10] by subdividing the data into three exclusive jet multiplicity categories: N Jets = 3-5, 6-7, and ≥8, which renders the analysis more sensitive to a variety of final-state topologies resulting from longer cascades of squarks and gluinos, and hence in a larger number of jets. The search regions with higher jet multiplicities extend the sensitivity of the analysis to models in which the gluino often decays into top quarks. While other analyses exploit the presence of bottom-quark jets in signal events to discriminate against background [12,13], this analysis follows a complementary strategy by requiring a large number of jets, thus helping to keep the signal efficiency for fully hadronic final states as high as possible.
The events in each jet multiplicity category are further divided according to variables that characterize the total visible hadronic activity (H T ) and the momentum imbalance (H T / ) in an event, both defined in the plane transverse to the beam. Due to the presence of a number of energetic jets and two LSPs in the final state, the signal events are expected to have large H T and H T / . The main SM processes contributing to this final state are Z+jets events, where the Z boson decays to a pair of neutrinos (Z(νν)+jets), and W+jets and tt events, where a W boson decays to an e, µ, or τ lepton (W( ν)+jets). The presence of at least one neutrino in these events provides a source of genuine H T / . Another background category is quantum chromodynamics (QCD) multijet events with large H T / from leptonic decays of heavy-flavour hadrons inside the jets, jet energy mismeasurement, or instrumental noise and non-functioning detector components.
• Events containing isolated muons or electrons with p T > 10 GeV are vetoed in order to reject tt and W/Z+jets events with leptons in the final state. Both the e and µ are required to produce a good quality track that is matched to the primary interaction vertex [30,31]. The isolation is measured as the scalar p T sum of PF particles (p sum T ), except the lepton itself, within a cone of width ∆R = √ (∆η) 2 + (∆φ) 2 = 0.3 for e (0.4 for µ) around the lepton. The p sum T is required to be less than 20% (15%) of the p T of the e (µ).
• In addition, events affected by instrumental effects, particles from non-collision sources, or poorly reconstructed kinematic variables are rejected (event cleaning) [28,29]. Events are also rejected if a jet with p T > 30 GeV has more than 95% of its energy from PF photon candidates or more than 90% from PF neutral hadron candidates.
The data sample used for this analysis was collected using trigger algorithms that required events to have H T > 350 GeV and E T / > 100 GeV. The trigger efficiencies are measured to be greater than 99% for the offline baseline selection of H T > 500 GeV and H T / > 200 GeV in all jet multiplicity categories used in this search. A sample of 11 753 events is selected after applying the baseline criteria. The selected events are divided into 36 non-overlapping search regions defined in terms of N Jets , H T , and H T / , as listed in the first three columns of Table 1.
Several Monte Carlo (MC) simulation samples are used to model the signal as well as to develop and validate the background estimation methods. The tt, W/Z+jets, γ+jets, and QCD multijet background samples are produced using the MADGRAPH5 [32] generator at leading order (LO), interfaced with the PYTHIA 6.4.24 [33] parton-shower model, and scaled to the next-to-leading order (NLO) or next-to-next-to-leading order cross section predictions [34,35].
The events are processed through a GEANT4 simulation of the detector [36]. The SUSY signal samples are generated using MADGRAPH5, the CTEQ6L [37] parton distribution functions (PDF), and are simulated using the CMS fast simulation package [38]. The underlying event description used for the MC simulated samples is described in Ref. [39]. The effect of pileup interactions is included by adding a number of simulated minimum bias events, on top of the hard interaction, to match the distribution observed in data.

Background estimation
In this search, all backgrounds are measured from data using methods similar to those described in Refs. [9, 10]. The Z(νν)+jets background is estimated using γ+jets events, exploiting their electroweak correspondence to Z+jets production for boson p T above ∼100 GeV. The Z+jets and γ+jets events exhibit similar characteristics, apart from electroweak coupling differences and asymptotically vanishing residual mass effects. The tt or W( ν)+jets events satisfy the search selection when the e/µ is not identified or isolated, or is out of the detector acceptance ("lost-lepton" background) or when a τ lepton decays hadronically (τ h background). The lost-lepton background is estimated by reweighting events in a µ+jets data control sample with measured lepton efficiencies. The estimation of the τ h background starts from a similar µ+jets sample, replacing the muon with a jet sampled as a function of jet p T from τ h templates obtained from simulation. The QCD multijet background is measured using a "rebalance-andsmear" method [9, 10]. The kinematical characteristics of multijet events are predicted from data by applying a fitting procedure that imposes zero missing transverse momentum on each event, and then smearing the jets according to data-corrected jet energy resolution values. The relative contribution of the various backgrounds varies in the different search regions.

Estimation of Z(νν) +jets background
Photons and Z bosons exhibit similar kinematic properties at high p T , and therefore the hadronic component of an event containing either a high-p T photon or Z boson is similar [40][41][42][43]. The γ+jets sample used to evaluate the Z(νν)+jets event rate is collected by triggering on events with a γ candidate and large H T . The photon candidates are reconstructed using the energy deposited in the electromagnetic calorimeter [44,45]. Photon candidates with p T > 100 GeV and |η| < 1.44 or 1.566 < |η| < 2.5 are used in this analysis, and are required to have their lateral shower profile consistent with that of a photon produced in the hard-scattering process (a prompt photon). To veto electrons misidentified as photons, the candidates with an associated track in the pixel detector are rejected. A photon candidate is required to satisfy tight isolation requirements based on the sum over p T values of the PF candidates that lie within a cone of radius ∆R = 0.3 around the direction of its momentum.
The contribution to the γ+jets control sample from events in which the photon candidate originates from the misidentification of jet fragments (background photons) is measured using a template method, which exploits the difference between the shower profile of prompt (signal) and background photons, using the distribution of a modified second moment of the electromagnetic energy cluster around its mean η position [44]. The distribution (template) for background events is obtained from a sideband region defined by selecting photons that satisfy very loose photon identification and isolation requirements but fail the stringent isolation requirements. The distribution for signal events is obtained from simulation. The sum of the two templates is fit to the observed distribution, with the normalization (background and signal yields) of each template determined in the fit. On average, 93% of selected γ+jets candidate events are determined to originate from prompt photons.
To mimic the missing momentum due to the neutrinos from the decay of the Z boson, the photon candidate is not included in the calculation of H T and H T / for the γ+jets events. The number of Z(νν)+jets events is then estimated by correcting the number of γ+jets events for photon acceptance and reconstruction efficiency, and scaling the result with the ratio relating the production cross section of the two processes (R Z/γ ) in the various search regions. Therefore, the ratio R Z/γ , which we derive from simulation, is studied as a function of H T , H T / , and N Jets using events generated with MADGRAPH (up to four partons) that are processed through the PYTHIA parton shower algorithm to generate additional jets. The ratio exhibits a strong dependence on H T / for values below around 500 GeV ( Fig. 1(a)), but changes by only (12 ± 5)% as H T varies between 500 and 1500 GeV ( Fig. 1(b)), which is the region of interest to this search. The ratio is parametrized as a linear function of N Jets in several H T / ranges, 200 < H T / < 300 GeV, 300 < H T / < 450 GeV, and H T / > 450 GeV, as shown in Fig. 1(c). The predicted numbers of Z(νν) +jets events and uncertainties for various search regions are summarized in Table 1.
The theoretical uncertainty associated with R Z/γ is estimated using Z(µ + µ − ) +jets events selected from data and simulation, by requiring two opposite-sign muons to satisfy the muon selection and to form an invariant mass within ±20 GeV of the Z boson mass. The double ratio of R Z(µ + µ − )/γ using events from data to those from simulation is parametrized as a function of N Jets using a linear function, as shown in Fig. 1(d), and is used to correct R Z/γ for a given jet multiplicity. The fitting procedure results in uncertainties of 20%, 25%, and 45% for the background predicted in the search regions with N Jets = 3-5, 6-7, and ≥8, respectively. The difference in the modeling of photon identification and isolation in the simulation and data leads to uncertainties of 2-5%, 10-20%, and 20-25% on the estimated number of Z(νν)+jets events for the three jet multiplicity intervals, respectively. The subtraction of events with nonprompt photons from QCD multijet events amounts to less than a 5% uncertainty for the final

Estimation of the lost-lepton background
The lost-lepton background is estimated from a µ+jets control sample, selected with the same criteria as used for the search, except that events are required to have exactly one well-reconstructed and isolated µ with p µ T >10 GeV. The events are collected with the same trigger that is used to search for the signal. The transverse mass ] is required to be less than 100 GeV in order to select events containing W → µν decays as well as to reject possible signal events. Here ∆φ is the azimuthal angle between the p T µ and the E T / directions. This method is validated using simulated tt and W+jets events. The single-muon events selected from the simulated samples are used to predict the number of background events expected in the zero-lepton search regions. The resulting H T , H T / , and N Jets distributions are compared in Fig. 2 to the genuine ones obtained from tt and W+jets events simulated at the detector level. The predicted distributions closely resemble the genuine ones.  The number of lost-lepton events predicted from data using the method described above, and the corresponding uncertainties, are listed in Table 1 for each search region. The dominant uncertainties arise from the limited number of single-muon events in most of the search regions. The differences in lepton reconstruction and isolation efficiencies between data and MC simulation are evaluated using a "tag-and-probe" method [46] on Z(µ + µ − )+jets events. The lepton reconstruction and isolation efficiencies are measured in bins of lepton p T and ∆R relative to the closest jet. This method renders these efficiencies insensitive to the kinematic differences between Z( + − )+jets events and tt and W+jets events. Relative differences between the predictions using efficiencies extracted from data and MC simulation result in 10-25%, 10-30%, and 15-24% uncertainties for the predicted background for various H T and H T / search bins with N Jets = 3-5, 6-7, and ≥8, respectively. An additional uncertainty of 15% for N Jets = 3-5 and 40% for N Jets ≥ 6 is assigned based on the statistical precision of the validation of this background estimation method. Variation of the PDFs following the procedure of Ref. [47] affects the muon acceptance, and leads to an uncertainty of less than 4% on the final prediction. Any mismodeling of anomalous E T / [28] affects the simulated m T and results in 3% uncertainty for the predicted lost-lepton background.

Estimation of the hadronic τ lepton background
The τ h background is estimated from a sample of µ+jets events, selected with an inclusive single µ or µ + ≥2-jet trigger, by requiring exactly one µ with p T > 20 GeV and |η| < 2.1. As in the estimation of the lost-lepton background, only events with m T < 100 GeV are considered. The µ+jets and τ h +jets events arise from the same physics processes; hence the hadronic component of the two samples is the same aside from the response of the detector to a muon or a τ h jet. To account for this difference, the muon is replaced by a simulated τ h jet, whose p T value is randomly sampled from an MC response function, p Jet T /p τ T . Here, the p τ T is the transverse momentum of a generated hadronically decaying τ lepton selected from simulated tt and W(τν)+jets events and p Jet T is that of a reconstructed jet matching the τ lepton in η-φ space. In order to sample the response function completely, this procedure is repeated one hundred times for each event. The N Jets , H T , and H T / values of the events are recalculated, now including this τ h jet, and search region selection criteria are applied to predict the τ h background. The predicted background is corrected for the trigger efficiency, muon selection efficiency, kinematic and detector acceptance, and the ratio of branching fractions B(W → τ h ν)/B(W → µν) = 0.6476 ± 0.0024 [48]. The muon isolation and reconstruction efficiencies are obtained from MC simulation of W+jets and tt events in bins of lepton p T and ∆R relative to the closest jet. To account for the difference in efficiencies measured in data and MC simulation, the predicted numbers of τ h +jets events are corrected by 4.9%, 4.7%, and 3.5% for N Jets =3-5, 6-7, and ≥8, respectively. The predicted τ h background and uncertainties are shown in Table 1 for all the search regions.  The τ h background estimation method is validated by applying it to simulated W+jets and tt MC samples. The results are shown in Fig. 3 in comparison to the genuine τ h background from the simulated events. To evaluate the performance of the method for events with varying hadronic activity, the method is validated in each search bin. Uncertainties of 10%, 20%, and 20% are assigned to the predicted rates for events with N Jets =3-5, 6-7, and ≥8 respectively, mainly to reflect the level of statistical precision for this validation. Due to the multiple sampling of the response template, the statistical uncertainty of the prediction is evaluated with a set of pseudo-experiments using a bootstrap technique [49]. Relative differences between the predictions using efficiencies extracted from data and MC result in 2-20% uncertainties across the various search bins. Other systematic uncertainties arise from the geometrical and kinematic acceptance for the muons (3%), and the τ-jet response function (1-15%). An uncertainty of 1-8% is assigned to account for possible differences between data and MC simulation for the acceptance of the m T selection.

Estimation of the QCD multijet background
The background from QCD multijet events is evaluated with the "rebalance and smear" method [9, 10], using data samples recorded with H T thresholds ranging from 350 to 650 GeV. The events, recorded with a trigger prescaled by a factor k, are sampled k times to create seed events as described below.
In the rebalance step, the momenta of the jets with p T > 10 GeV/c in each event are adjusted within the jet-p T -resolution values, using a kinematic fit, such that the events are balanced in the transverse plane. Considering only jets with p T above a certain threshold introduces an additional imbalance in the event, which results in larger p T for the rebalanced jets than the expected true value. This effect is compensated by scaling the rebalanced jets by a p Tdependent factor derived by comparing rebalanced and generator-level jets in the simulation. The scaling factors derived using either PYTHIA or MADGRAPH, and with different average pileup interactions, are found to be similar. The jets in the rebalanced events are then smeared using jet p T response functions, which are obtained from MC simulation as a function of p T and η, and adjusted to match those determined from dijet and γ+jets data [27]. The QCD multijet background is predicted by applying selection criteria on the kinematic quantities calculated from the smeared jets. The procedure is repeated one hundred times to evaluate the average prediction and its statistical uncertainty in each search region.  / , and (c) N Jets distributions found from applying the "rebalance-and-smear" method to simulated QCD multijet events (solid points) in comparison with the genuine QCD multijet background from simulation (shaded curve). The distributions are shown for events that satisfy the baseline selection, except that the H T / selection is not applied, and in addition H T > 1000 GeV is required for the events used in the H T / distribution. The statistical uncertainties are indicated by the hatched band for the expectation and by error bars for the prediction.

Events / GeV
The method is validated using simulated QCD multijet events. Comparisons of the H T , H T / , and N Jets distributions from the MC simulation to those predicted by the rebalance-and-smear method on the same simulated events are shown in Fig. 4. A systematic uncertainty of 11-86% is assigned based on the statistical precision attributed to the validation procedure, which is performed both in the search regions and in QCD-enriched data control regions defined either by 100 < H T / < 200 GeV or by inverting the |∆φ( p Jet1,2,3 T , H T / )| selection. Due to the limited number of events in individual search bins, this uncertainty is evaluated for each jet multiplicity bin for H T smaller or larger than 1000 GeV, inclusive over H T / . The uncertainty due to differences in the core and tails of the jet response functions between data and simulation results in uncertainties of 10-30% and 20-35%, respectively. An uncertainty of 3%, 8%, and 35% is assigned for search regions with N Jets = 3-5, 6-7, and ≥8, respectively, to account for the effect of pileup. The predicted QCD multijet background contributions to the search bins along with associated uncertainties are given in Table 1.

Results and interpretation
The predicted background event yields and the number of observed events are summarized in Table 1 and Fig. 5 for the 36 search regions. The data are consistent with the expected background contributions from SM processes. A slight excess of events is observed in the search bin with N Jets = 6-7, H T = 500-800 GeV, and H T / > 450 GeV, which is insignificant when the probability to observe a statistical fluctuation as large or larger in any of the search regions is considered.
The results are interpreted in the context of simplified models [21,22] of pair production of squarks ( q) or gluinos ( g). These particles decay directly, or via intermediate new particles, to quarks and an LSP, where the LSP is denoted as χ 0 1 in the following. The signal events are generated at LO using MADGRAPH5, with up to two additional partons. The cross sections are determined at NLO and include the resummation of soft gluon emission at the accuracy of next-to-leading-log (NLL) calculations [50][51][52][53][54][55]. Both for the generation of signal events and the calculation of q ( g) production cross section, the contribution of g( q) production is effectively removed by assuming the gluino (squark) mass to be very large.
Several decay modes of gluinos are considered here, g → qq + χ 0 1 , g → tt + χ 0 1 , and g → qq + χ ± / χ 0 2 where χ ± 1 → W + χ 0 1 and χ 0 2 → Z + χ 0 1 . The branching fraction for the different decay modes is assumed, in turn, to be 100%, except for the g → qq + χ process, where the decay proceeds via χ + 1 , χ − 1 and χ 0 2 particles with equal probability. Squark production is studied in the decay mode q → q + χ 0 1 . The models are studied in the parameter space of the mass of the LSP versus the mass of the gluino or squark. The H T / distributions observed for the three intervals of jet multiplicity are shown in Fig. 6  The 95% confidence level (CL) upper limits on the signal production cross section are set using the LHC-style CL s criterion [56][57][58]. The signal acceptance and efficiencies, and corresponding uncertainties for the 36 exclusive search regions, along with the background estimates discussed above, are combined into a likelihood that is used to construct the test statistic based on the profile likelihood ratio. The uncertainties of the signal acceptance and efficiency due to several sources are taken into account when cross section upper limits are determined. The uncertainties due to the luminosity determination (2.6%) [59], trigger inefficiency (2%), and event cleaning procedure (3%) [28] are the same for all signal models and search regions. The uncertainty from the measurement of the jet energy scale and jet energy resolution [27] leads to uncertainties of 2-8% and 1-2% in signal acceptance. The variation of PDFs [47] results in 1-   )+jets )+jets  8% uncertainty from the signal acceptance. The rate of initial-state radiation in the signal event simulation is corrected to correspond to that measured in data [60], leading to a corresponding uncertainty of 22% for model points with small differences between the masses of the gluino or squark and the χ 0 1 . For larger mass differences, this uncertainty is typically less than a few percent.
The observed and expected 95% CL upper limits on the signal cross section are shown for the production of a q q pair with q → q + χ 0 1 in Fig. 7(a), a g g pair with g → qq + χ 0 1 in Fig. 7(b), a g g pair with g → tt + χ 0 1 in Fig. 7(c), and a g g pair with g → qq + W/Z + χ 0 1 in Fig. 7(d), in the (m q , m χ 0 1 ) and (m g , m χ 0 1 ) planes. The contours show the exclusion regions for the signal production cross sections obtained using the NLO+NLL calculations. The exclusion contours are also presented when the signal cross section is varied by changing the renormalization and factorization scales by a factor of two and using the PDF uncertainty based on the CTEQ6.6 [61] and MSTW2008 [62] PDF sets. Conservatively, by comparing the observed limit to the theoretical cross section minus its one-standard-deviation uncertainty, for the cases where the gluino decays as g → qq + χ 0 1 , g → tt + χ 0 1 , and g → qq + W/Z + χ 0 1 , gluino masses up to 1.16, 1.13, and 1.21 TeV are excluded, respectively, for m χ 0

Summary
An inclusive search for supersymmetry has been performed in multijet events with N Jets = 3-5, 6-7, and ≥8, and large missing transverse momentum. The data sample corresponds to an integrated luminosity of 19.5 fb −1 collected in 8 TeV pp collisions during the year 2012 with the CMS detector at the LHC. The analysis extends the supersymmetric parameter space explored by searches in the all-hadronic final state. The observed numbers of events are found to be consistent with the expected standard model background, which is evaluated from the data. The results are presented in the context of simplified models, where final states are described by the pair production of new particles decaying to one, two, or more jets and a weakly interacting stable neutral particle, e.g. the lightest supersymmetric particle (LSP). Squark masses below 780 GeV and gluino masses of up to 1.1-1.2 TeV are excluded at 95% CL within the studied models for LSP masses below 100 GeV.   [14] ATLAS Collaboration, "Search for squarks and gluinos with the ATLAS detector in final states with jets and missing transverse momentum using 4.7 fb −1 of √ s = 7 TeV proton-proton collision data", Phys. Rev. D 87 (2013) 012008, doi:10.1103/PhysRevD.87.012008, arXiv:1208.0949.