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 dijet 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 +  n-jet events
8.2 Estimating N_2^W
8.3 Estimating N_3^W
9 Results
%Events/bin
Number Events/10 fb-1
Number Events/10 fb-1
%Events/bin
%Events/bin
Number Events/10 fb-1
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10 Conclusion
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Acknowledgments
Appendix: Smoothing Method for Datasets with Low
Generated Statistics
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