Search for Supersymmetry in Events with b Jets and Missing Transverse Momentum at the LHC

A search for supersymmetry is presented using a sample of events with b jets and missing transverse momentum. The search uses a data sample of proton-proton collisions at a centre-of-mass energy of 7 TeV, corresponding to an integrated luminosity of 35 inverse picobarns, collected with the CMS detector. A total of 0.33 +0.43 -0.33 (stat.) +/- 0.13 (syst.) events is predicted, using control samples in the data, to arise from standard model processes, and one event is observed in the data. Upper limits are set at the 95% confidence level on the cross sections of benchmark supersymmetric models.


Introduction
Supersymmetry (SUSY) [1][2][3][4][5] is an extension of the standard model (SM) of particle physics, which can solve the "hierarchy problem" [6,7] and provide a candidate for cold dark matter [8]. For a large class of supersymmetric parameter sets, squarks (q), the SUSY partners of quarks, are relatively light. In this case, significant event yields at the Large Hadron Collider (LHC) can result from strong production of squarks, which subsequently decay giving a weakly interacting lightest supersymmetric particle (LSP). If bottom and top squarks, which can decay to b quarks, are relatively light, there may be an abundance of events with one or more b-quark jets and momentum imbalance transverse to the beam line due to the undetectable LSPs.
This Letter describes a search for events with two or more hadronic jets, at least one of which must be b tagged [9], and significant transverse momentum imbalance. It extends a similar search without a b-tag requirement [10]. The momentum imbalance is characterized [11] by the ratio of the p T of the second-highest-p T jet and the invariant mass formed from the two highestp T jets. This ratio can be estimated by α T = 1 The main backgrounds are due to standard model multijet production (hereafter denoted "QCD background"), electroweak W and Z boson production (EWK), and top quark pair production (tt). Owing to low average H / T , the QCD background is effectively rejected by a requirement on α T . The b-tag requirement further suppresses the QCD and EWK backgrounds.
The results of the search are characterized in terms of the mSUGRA/CMSSM [12,13] scenario of SUSY. These models are described by four parameters and one sign: the universal scalar and gaugino mass parameters, m 0 and m 1/2 , respectively; the universal trilinear coupling, A 0 ; the ratio of the two Higgs doublet vacuum expectation values, tan β; and the sign of the Higgs mixing parameter, sign(µ). Three signal points are considered as benchmarks: LM0, LM1, both discussed in Ref. [10], and LMB (corresponding to m 0 = 400 GeV, m 1/2 = 200 GeV, A 0 = 0 GeV, tan β = 50, and sign(µ) > 0), chosen to be near the edge of sensitivity of this search in mSUGRA/CMSSM parameter space.
The analysis presented here uses a data sample of proton-proton collisions at 7 TeV, corresponding to an integrated luminosity of 35 pb −1 , collected with the Compact Muon Solenoid (CMS) detector, at the LHC. The main components of CMS are a silicon pixel and strip tracker, the crystal electromagnetic calorimeter, and the brass/scintillator hadron calorimeter, all placed in a 3.8 T axial magnetic field, complemented by gas-ionization detectors embedded in the steel return yoke, to measure muons. A detailed description of the detector and its performance can be found in Ref. [14]. In the cylindrical coordinate system of CMS, φ is the azimuthal angle and the pseudo-rapidity (η) is defined as η = − ln [tan (θ/2)], where θ is the polar angle with respect to the counterclockwise beam direction.

Event Selection
The event selection requirements are mostly identical to those in Ref. [10]. Events in the search sample are collected with triggers based on H T computed from jets reconstructed at trigger level. A muon-enriched control sample is collected with triggers requiring a muon. Events 2 3 Background Estimation must have a good reconstructed pp collision vertex [15]. Jets are reconstructed as clusters of energy in the calorimeters by the anti-k T algorithm [16] with a distance parameter of 0.5, and are required to have energy transverse to the beam, E T , in excess of 50 GeV and |η| less than 3.
To perform a fully hadronic final state search and to reduce the backgrounds, events with an isolated lepton (electron or muon) or photon are vetoed, and events consistent with having apparent H / T [10] are rejected. Selected events are required to have at least two jets, both with E T > 100 GeV, |η| < 2.5 for the highest-E T jet, H T > 350 GeV, at least one jet tagged as originating from a b quark, and α T > 0.55.
Jets are b tagged using a discriminator based on the impact parameter significance of tracks in a jet (Track Counting High Purity discriminator, TCHP [9]), with a "tight" selection (TCHP> 3.41) designed to have a light-flavour contamination of less than 0.1%. Looser b-tagging selections are used to produce various control samples. An event is said to be anti-tagged if it contains no jets with a loose b tag (TCHP > 1.19). To remain within the acceptance of the pixel tracker, only jets with a central axis of |η| < 2.4 are considered for b tagging.

Background Estimation
The backgrounds for this search can be categorized into three main groups: namely QCD, EWK, and tt. The contamination from tt is mainly in the tau decay mode. The vast majority of events from the QCD background do not feature large transverse momentum imbalance and are therefore rejected by the α T > 0.55 requirement. The EWK backgrounds consist of W and Z boson production, with genuine missing energy due to decay neutrinos. The requirement of at least one b jet greatly reduces the EWK and QCD backgrounds. The dominant background for the analysis arises from tt production, in which b jets and genuine missing energy due to neutrinos can arise from the top quark decay chains.
A procedure based on control data samples, described in Section 3.1, is employed to estimate all backgrounds simultaneously. In this method, the fraction of all events with α T > 0.55, denoted F(α T > 0.55), is measured in a lower-H T control region and applied in the signal region.
The Z → νν and tt background yields are cross-checked separately, as discussed in Section 3.2. The tt cross-check uses muons to emulate the hadronic decays of taus. The cross-check of Z → νν utilizes Z → µ + µ − events for which α T is determined after excluding the muons.

Background Prediction Using α T vs H T Extrapolation
In SM simulation studies [10], F(α T > 0.55) has no H T dependence in events with large genuine missing transverse energy, i.e., the tt and EWK backgrounds. In the QCD background, however, F(α T > 0.55) is expected to be a decreasing function of H T because of the H T dependence of the factors contributing to apparent H / T , such as jet energy resolution and jet E T threshold effects.
In data control samples, F(α T > 0.55) is consistent with having no H T dependence, which indicates that the tt and EWK backgrounds dominate. The larger anti-tagged data sample is also consistent with having no H T dependence. Because a tight b-tag requirement further suppresses the QCD background, the tight tagged data sample is expected to have a negligible QCD contribution and therefore F(α T > 0.55) independent of H T .
The total background is estimated by measuring F(α T > 0.55) = 1.48 +1.93 −1.48 × 10 −5 in a control region with 250 < H T < 350 GeV and multiplying this fraction by the number of events in the signal region before the α T > 0.55 requirement. In data, this procedure yields a prediction of  Figure 1: The α T distributions for Z → µ + µ − emulation of Z → νν (solid blue) and muon emulation of hadronic tau decays (dashed red). 0.33 +0.43 −0.33 (stat.) ± 0.13 (syst.) events. The statistical uncertainty is dominated by the presence of one event with α T > 0.55 in the control sample. The systematic uncertainty on the prediction is given by the difference in F(α T > 0.55) measured in the tight and loose tagged control samples. Table 1 lists this background prediction, the observation in data, and the expected contribution of SUSY signal for points LM0, LM1, and LMB.

Cross-Checks of Z → νν and tt Background Contributions
While the above background estimate is the one used in this search, we perform auxiliary measurements to cross-check the Z → νν and tt background components, which together are expected to comprise the majority of the background. As would be crucial in case of an observed excess, these cross-checks provide an overestimate of the Z → νν and tt background components.
For Z → νν, a sample of Z → µ + µ − events is selected with two or more jets but no α T , H T , or btagging requirements. The solid blue line in Figure 1 shows the α T distribution for the resulting events. The fraction of these events containing a b-tagged jet is measured. Then, a sample is selected with no b-tag requirement, jet E T = 75 GeV thresholds on the two highest-E T jets, H T > 275 GeV, and α T > 0.52. The number of events in this sample is scaled by the measured b-tag fraction in the other sample, corrected for the muon identification efficiency and acceptance, and multiplied by the ratio of branching fractions BR(Z → νν) BR(Z → µ + µ − ) ≈ 6. This procedure gives an overestimate of the number of Z → νν events in the signal region owing to less stringent requirements than in the final selection, and yields 0.48 ± 0.39 events.
Simulation studies indicate that most of the tt background comes from events with hadronic tau decays. To estimate the hadronic tau decay yield, F(α T > 0.55) is first measured in a sample with E T = 80 GeV thresholds on the two leading jets, H T > 280 GeV, at least one medium btagged jet (TCHP > 1.91), and one or two muons. These selection requirements are chosen to be less strict than the signal selection in order to increase the number of events in this sample. The muons are used to emulate the hadronic decays of taus. To do so, for each muon the presence of a tau jet is emulated with an E T value set to a fraction of the muon p T , using a distribution taken from simulation. The dashed red line in Figure 1 displays the resulting α T distribution. The measured value of F(α T > 0.55) in this sample is multiplied by the number of emulated events in the signal region before the α T requirement. This value is corrected for the muon selection efficiency, acceptance and the hadronic tau decay branching ratio to obtain the hadronic tau decay yield. The predicted hadronic tau decay yield is increased by 38%, as determined in simulation, in order to account for the entire tt background. The procedure yields a 25% overestimate of the total tt background in simulation. In data, 1.4 ± 0.5 events are predicted.

Signal Selection Efficiency
To interpret the results of this search in terms of a given signal model, the selection efficiency for that model must be determined. Table 2 lists the cumulative and individual efficiencies for the event selection in the three SUSY benchmark models LM0, LM1, and LMB, from which events are generated at leading order (LO) via PYTHIA 6.4, tune Z2 [17] using parton distribution functions provided by CTEQ6. 6 [18]. Without b tagging, the cumulative efficiencies for LM0 and LM1 are about 85% of those in Ref. [10], because of a more stringent lepton and photon veto. Table 3 lists the relative systematic uncertainties on the signal yield, which are dominated by the uncertainty on the b-tagging efficiency, described below. The other uncertainties and the methods used to obtain them are similar to Ref. [10].
The b-tagging efficiency is measured from inclusive dijet events in which one jet has an associated muon and another "away" jet has a TCHP value of at least 1.0. The relative fraction of jets from b quarks in a data sample is determined by a fit to the distribution of transverse momentum of muons relative to their associated jet axis, p rel T [9,19], which is larger for jets from b quarks than from other flavours. This fit is to a linear combination of simulation-derived p rel T expected distributions from different flavours. The fitted b fractions for jets passing and failing the analysis b-tagging requirement are used in the b-tagging efficiency calculation. This efficiency is measured separately for jets with |η| > 1.4 and |η| ≤ 1.4, in four ranges of jet E T . The ratio between the b-tagging efficiency measured in data and in simulation is taken as the efficiency scale factor for a particular range in E T and |η|.
Systematic uncertainties on the scale factors arise from potential biases in the p rel T fitting procedure. These uncertainties are measured by varying the muon-to-jet matching and muon p T thresholds, fraction of gluon splitting to bb, jet energy scale and resolution, jet angular resolution, and b-tagging requirement on the away jet. The effect of measuring the scale factors using only semi-leptonic b decays is also accounted for. The scale factors are used to correct the expected event yield at each signal point for differences between the efficiencies in data and simulation. For example, for LMB the application of the scale factors translates into a change in the yield by a factor 0.87 ± 0.18. The systematic and statistical uncertainties give a total relative uncertainty of 20% in LMB, with a similar uncertainty of 23% in LM1.

Results
The observation of one data event in the signal region is consistent with background expectations. Combining the expected signal and background prediction from Section 3.1 and using frequentist statistical methods in the manner of Ref.
[20] with the Profile Likelihood ratio [21] to handle nuisance parameters, we derive 95% confidence level (CL) cross-section upper limits (σ obs 95 ) of 18.9, 15.4, and 10.2 pb for LM0, LM1, and LMB, respectively. The effect of possibly overestimating the background due to signal contamination in the control regions increases the σ obs 95 value to 22.1 pb for LM0, 16.7 pb for LM1, but is negligible for LMB. To quantify the sensitivity with reduced dependence on the amount of b-quark production, a 95% CL upper limit on the cross section times branching ratio to at least one b quark of 4.0 pb is determined in LM1.
The resulting excluded region in the (m 0 , m 1/2 ) plane for a reference model with CMSSM parameters A 0 = 0 GeV, tan β = 50, and µ > 0 is shown in Figure 2. The expected and observed exclusion regions are calculated using next-to-leading-order (NLO) cross sections, obtained with the program Prospino [22]. The excluded region is extended with respect to that of Ref. [10] without b tagging, also shown, for scenarios with increased b production, such as those with m 0 above 350 GeV.

Summary
A search for events with multiple jets, at least one of which is b tagged, and significant transverse momentum imbalance has been presented. One event is observed, which is consistent with background expectations. The dominant background comes from tt production.