CMS Discovery Potential for Low Mass mSUGRA in Single-muon (Same Sign Di-muon) Events with Jets and Large Missing Transverse Energy in pp Collisions at sqrt(s) = 14 TeV
1 Introduction
2 The CMS Detector
3 Event Simulation
3.1 Signal
The minimal extension to local Supersymmetry is
3.2 Backgrounds
The following backgrounds were considered…
Dijet QCD Backgrounds
ttbar backgrounds
Single-boson + jets backgrounds
Di-boson + jets backgrounds
4 Online and Event Pre-selection
Event selection at CMS is performed at two levels: online selection at the trigger level and offline selection at the analysis level. The algorithms to reconstruct the physical objects (muon, jet, MET) as well as their identification at the online and offline levels are described in Ref. [??]. We summarize below the selections pertaining to this analysis.
4.1 Triggers
The CMS trigger system is composed of a hardware-based Level-1 Trigger System and a software-based High Level Trigger (HLT) System: Level-1 reduces the input interaction rate of 1 GHz to a filtered event rate of 75 kHz, whilst the HLT uses the full event information to further reduce the event rate to 100 Hz written to mass storage. This work uses event samples which are defined by two HLT triggers: the inclusive single-muon and di-muon triggers (see Table ??).
A single-muon inclusive trigger is formed by requiring that either (1) in the endcaps low quality Level-1 Cathode Strip Chamber (CSC) tracks be matched with Resistive Plate Chambers (RPC) tracks by the Global Muon Trigger and at least one Level-2 muon be reconstructed with a valid extrapolation to the collision vertex, or (2) in the barrel at least one Drift Tube (DT) track segment be reconstructed with the sum of the number of DT segments and RPC hits greater than three. At Level-3, a muon must have more than five tracker hits. Finally, for the HLT, the Level-2 muon must satisfy calorimeter isolation (at the 97% efficiency point), and the Level-3 muon must satisfy the tracker isolation (at the 97% efficiency point).
A di-muon inclusive trigger is formed by the same criteria as for the single-muon trigger, but the isolation criteria are relaxed so that only one of the two muons need satisfy it. Further, at Level-3, both muons are required to originate from the same vertex (within 5 mm) and di-muons which are close in space/momentum (dphi < 0.05, deta<0.01, dpt<0.1 GeV) are rejected to remove ghost tracks.
For low-luminosity running, the single-muon trigger pt threshold is set at Level-1 to be 14 GeV, corresponding to 2.7 kHz (unscaled) and 95% efficiency, and at HLT to be 19 GeV, corresponding to 25 Hz (unscaled) and 90% efficiency. The symmetric pt threshold for the di-muon trigger is lowered at Level-1 to be 3 GeV, corresponding to a rate of 0.9 kHz (unscaled) and 95% efficiency, and at HLT to be 7 GeV, corresponding to a rate of 4 Hz (unscaled) and 90% efficiency.
We have studied the effects of including a single-muon + MET and single-muon + Jet trigger in the CMS trigger menu…
4.2 Object Identification
The CMS reconstructed objects…
4.2.1 Muons
CMS uses “Regional Reconstruction” algorithms which enable “offline” muons to be reconstructed in the same way as “online” muons (those selected by the HLT). Muon reconstruction is seeded by the four candidates found by the Level-1 muon trigger. A “forward” Kalman-filter technique is used, moving from the inner muon chambers to the outer muon chambers, followed by a “backward” Kalman-filter (moving outside to inside). The track is extrapolated to the nominal interaction point and a vertex constrained fit is performed. Next, the track is extrapolated to include hits in the silicon and pixel trackers using the following steps: seeded pattern recognition is used to first build the trajectory, resolution of ambiguities are used to clean the trajectory, and a final fit is performed. The list of final muon candidates is then made by cutting on the chi2 of each trajectory. The selected candidates are then refitted, excluding hits with high residual values in muon stations with high occupancy. Very high pt (TeV) muons are …. (This whole section needs to be worded much more precisely)
4.2.2 Jets
Jets are reconstructed using the Iterative Cone algorithm applied to calorimeter towers in which the energy from ECAL and HCAL are added together. Because the HCAL has a significantly coarser granularity than ECAL, a single HCAL tower in the barrel corresponds to 25 (5x5) ECAL crystals; due to geometry considerations, a more complex association of HCAL towers to ECAL crystals is required in the end-caps. In this work, a cone of size R = 0.5 in eta, phi space around an input tower seed of at least 1 GeV is used to define a “proto-jet”. The ET scheme is used to calculate the jet momenta. An iterative procedure is then applied in which the direction of “proto-jets” seed new “proto-jets”. Convergence to a “jet” is defined to occur once the change between iterations in proto-jet energies is less than 1% and Delta R < 0.01. The list of towers used to define the “jet” is then removed from further consideration and the procedure is repeated until no more seed towers exist with an ET above 1 GeV.
The reconstructed jets are calibrated using photon+Jet events…
4.2.3 Missing Transverse Energy
The Missing Transverse Energy (MET) of each event is reconstructed by taking the negative vector sum over all calorimeter towers in the transverse plane.
Corrections due to minimum ionizing muons were investigated, but rejected due to uncertainties in the behavior of high-PT reconstructed muons. Hence, no corrections are applied to the MET.
4.3 Pre-selection of Offline Datasets
To ensure a minimal understanding of the physics objects used in this work, quality criteria are applied to muons, jets, and MET. The leading muon is required to have a pT above 30 GeV which ensures that the muon candidate is reconstructed with good efficiency, well above the thresholds of 19 GeV in the single-muon trigger and 7 GeV in the di-muon trigger. Further the leading muon is required to be isolated with less than 5 GeV of calorimeter energy within a cone of radius 0.3 reducing the effects due to fake muons. The three leading jets must each have an ET of at least 50 GeV which guarantees that the jets are reconstructed with good efficiency. Finally, the Missing ET is required to be at least above 50 GeV in order to reduce effects due to fake MET.
5 Discriminating Signal from Background
Because the supersymmetry has not yet been observed in nature, if it exists it must be a broken symmetry. Results from LEP and the Tevatron imply that the mass difference between sparticles and particles must be relatively large, leading to long decay chains involving many relatively hard jets.
Further, in this analysis we assume R-parity conservation which means that the lightest supersymmetric particle (LSP) is stable. This leads to one of the most distinguishing characteristics of the signal, that of large missing transverse energy.
In order to distinguish between events with large true MET and events with large fake MET, due to jet energy resolution for example, another distinguishing feature between signal and background is that the MET direction should neither be opposite the leading jet nor second leading jet.
Because the jet directions from SUSY are not strongly correlated, one also expects that the leading and second leading jet should not be back-to-back, as would be the case of di-jet QCD events with no FSR. Finally, owing to the high pT nature of the SUSY jet spectrum, one expects that jets will be more centrally located.
6 Treatment of Systematic Uncertainties
6.1 Finite Monte Carlo Statistics
The effective number of events used in this analysis from each Monte Carlo sample is calculated by weighting each event according to its cross-section and the assumed luminosity. For high cross-section process, this can lead to events with high weights, and hence large uncertainties on the predicted background level. It may be shown that the uncertainty due to finite generation of statistics for a particular Monte Carlo sample is given by Nw(sel) / sqrt(Ngen), where Nw(sel) is the luminosity and cross-section weighted number of events which pass the selection cuts and Ngen is the total number of generated (unweighted) events for the sample. As an example, Figure X shows that, while the QCD cross-section rapidly falls as a function of pt_hat, the Monte Carlo QCD datasets used in this analysis were generated approximately flat in pt_hat. Figure Y, shows the corresponding uncertainty in predicting the QCD background due to the finite Monte Carlo statistics generated for each QCD dataset. For low pT_hat, one clearly sees that generating enough QCD to match the expected cross-section is hopeless. It is thus vital that cuts are imposed in this analysis which rejects low pt_hat QCD. On the other hand, with an integrated luminosity of 10 fb-1, one expects to see only a very small fraction of QCD events for large pT_hat, and so one can safely ignore the Monte Carlo samples for very high pt_hat. Given that one can reject low pt_hat QCD events, the important pt_hat region corresponds to where the QCD cross-section is comparable to the assumed integrated luminosity of 10 fb-1.
6.2 Jet Energy Scale
This analysis uses the ET of the three leading jets as well as the Missing ET of the event as variables which discriminate between the mSUGRA signal and the Standard Model background. Hence, uncertainties in the Jet Energy Scale can lead to systematic uncertainties in the estimated significance for possible discovery or the estimated confidence level for possible exclusion. Reference [ref] estimates that by 10fb-1 of integrated luminosity, the CMS Jet Energy Scale will be calibrated to within 5% using photon-jet balancing. Accordingly, we apply a scaling of the jet ET’s and the MET (assuming 100% correlation between the Jets and the MET) by +5% and -5%. The number of events which pass in the systematically altered case is compared with the number of events which pass in the unaltered case and the systematic uncertainty, due to jet energy scale, is then taken as the difference between the two cases.
6.3 Jet energy Resolution
Similar to the Jet Energy Scale, uncertainties in the Jet Energy Resolution can lead to systematic uncertainties in the estimated significance for possible discovery or the estimated confidence level for exclusion. Reference [ref] estimates that by 10fb-1 of integrated luminosity, the resolution of CMS jet energies will be known to within 5% using di-jet balancing. Accordingly we apply a Gaussian smearing of the jet energies, worsening them by 5% of their original resolution. The MET two-vector is assumed to be 100% correlated with the jets, and MET two-vector is correspondingly modified, event-by-event, according to the smeared jet energy. The number of events which pass in the systematically altered case is compared with the number of events which pass in the unaltered case and the systematic uncertainty, due to jet energy scale, is then taken as the difference between the two cases.
6.4 Muon ID efficiency and fake rate
6.5 Luminosity
7 Search for Signal
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7.1 Significance Estimator
7.1.1 Regions dominated by systematic effects
7.1.2 Regions dominated by statistical effects
7.2 Genetic Algorithm Analysis
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8 Calibration to Standard Model Control Regions
8.1 Estimating the number of W + ³ n-jet events
8.2 Estimating N_2^W
8.3 Estimating N_3^W
9 Results
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10 Conclusion
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Acknowledgments
Appendix: Smoothing Method for Datasets with Low Generated Statistics
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