for NVertices = 1 and is increasing linearly to ≈ 19 GeV/c for NVertices = 18. The transverse component has the same behavior.
Figure 3.15: ETmiss resolution as a function of the transverse momentum of the Z boson (qT), when induced ETmissin Z → µ+µ−events by removing the vector boson [182]. The ETmiss resolution is shown in both parallel and transverse directions to the axis of the transverse momentum of the Z boson. In this analysis, data of run 2011A are used.
The observation is that the ETmiss-resolution components are well simulated for events with more than five reconstructed vertices in both parallel and transverse directions. However, the resolution is worse in data for events with less than five vertices. The resolution of both com-ponents is found to be 7% worse for events with exactly one reconstructed primary vertex, and 4% worse for events with exactly three reconstructed primary vertices. The observed resolution in data as a function of qTagrees well with the simulated resolution by 5% for qT < 50GeV for both components. These findings are consistent with the result from studies with events at low Pile-Up conditions (cf. [175]).
In conclusion, ETmissis found to be reasonably well understood and ready to be used in CMS high-precision analyses including top-quark analyses [175]. The varied ETmiss resolution be-tween data and simulation, which also propagates to the ETmissresponse, is covered with corre-sponding uncertainties and discussed in section 6.1.6.
3.4 Collision Data and Luminosity Determination
Recorded collision data are categorized into several datasets already at the HLT level. Each trigger belongs to a certain dataset. In this analysis, datasets are used that correspond to single-muon triggers, single-electron triggers, and triggers that require an electron and hadronic ac-tivity. Technically speaking, the SingleMu, SingleElectron, and ElectronHad datasets of the proton-proton run Run2011A are analyzed.
The CMS-data certification ensures that the subdetectors, subsystems, and physics objects reconstruction were operational and that they performed as expected. Thus, it ensures a good
quality of the data used for physics analyses. Data are certified in units of luminosity sections of a certain run; a “luminosity section” refers to a 23.3-s-long data-taking period in which the instantaneous luminosity remains nearly constant [183]. Only data that are officially certified by CMS are used in this analysis.
Many techniques for luminosity determination exist, including techniques that provide measurements either online for real-time performance monitoring or offline for an absolute normalization as used in high-level-physics analyses. In the following, a brief overview of the usual methods to determine the luminosity, which is recorded by the CMS detector, is given, and the luminosity determination as used in this analysis is briefly discussed.
One measure of luminosity is based on the HF calorimeter [153, 184, 185], since every in-teraction deposits energy in the HF calorimeter well above the noise level. The number of interactions itself is correlated to the luminosity. Two methods exist that make use of the HF calorimeter. The first method is based on counting the (average) number of “empty” HF tow-ers, i.e. towers in which no energy is deposited. The number of occurring interactions in each bunch crossing follows Poisson statistics, and HF towers can be used to check whether an inter-action occurred or not. However, the HF is not directly sensitive to the number of interinter-actions that occurred, but can distinguish between zero or more interactions. Instead of counting the number of HF towers, the number of “empty” towers is used to determine the number of in-teractions with inverted Poisson probability. Additional sensitivity comes from the fact that all HF towers are statistically independent among each other. The second method makes use of the linear correlation between the deposited transverse energy ET in the HF towers and the number of interactions. Van der Meer (VdM) scans are used for an absolute calibration of the luminosity with minimal model dependence.
In a VdM scan [186], which was originally conceived by S. Van der Meer for the “Intersecting Storage Rings” at CERN in 1968, the absolute luminosity is deduced from machine parameters only. The two beams are displaced against each other in the transverse plane, while monitoring the relative beam-beam-interaction rate. Then, the instantaneous luminosity can be expressed as a function of the beam separation, the beam profile (i.e. the size and shape of the proton density in the beam), the bunch intensity, and the LHC-orbit frequency f . The bunch intensity is determined externally with measurements using Fast Beam Current Transformers [184]. The LHC-orbit frequency (also referred to as “revolution frequency”) is a general parameter of the LHC storage ring, which is f = 11.245 kHz [130]. Measuring the collision rate and fitting the observed beam-separation dependence allows the peak instantaneous luminosity to be deter-mined, as well as the effective beam size of the two beams. A double-Gaussian-beam profile describes the observed VdM-scan curves well [184]. The parametrization of the beam sizes in both x and y directions needs subsequent (separate) scans. However, the beam width evolves with time, and the emittance needs to be corrected accordingly [184].
A luminosity measurement with the HF calorimeter has the advantage that it allows for an online measurement. However, it has a non-linear response w.r.t. the instantaneous luminosity and a large sensitivity to the beam intensity. The total systematic uncertainty of the measured integrated luminosity is 4.5% [184] when using the HF-based luminometer.
Alternative determinations of luminosity include normalizations to measured cross sections of “standard-candle processes” like W-boson or Z-boson production [153]. Furthermore, the primary-vertex-production rate can be counted to derive a luminosity measurement, either by simply counting vertices or by deriving it (with Poisson statistics) from events in which no vertex is found [184]. Moreover, the TOTEM experiment uses the optical theorem to provide a complementary luminosity measurement [153].
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3.4 Collision Data and Luminosity Determination
In this analysis, the integrated luminosity in each luminosity section is calculated offline using a method that is based on pixel-cluster counting. The pixel-cluster cross section itself is a function of the integrated luminosity, mean number of observed pixel clusters, and the revolution (orbit) frequency f (see above). The absolute calibration of the pixel-cluster cross section is done with VdM scans. Here, the data are recorded using zero-bias triggers, i.e. using totally inclusive triggers. Since the number of pixels in the tracker is large, the probability that two tracks of the same bunch-crossing hit the same pixel is small. Therefore, the actual number of counted pixel clusters in a collision, divided by the pixel-cluster cross section, can be used as a measure of luminosity.
The estimated total uncertainty of the luminosity measurement is 2.2% [183]. The dominant uncertainties are the scan-to-scan variations (1.5%) and afterglow of the beam (1.0%) [183].
“Scan-to-scan” variations include two effects of the VdM scans. First, the measured pixel-cluster cross section spreads by 1.2% in a pair of two subsequent scans. Second, potential shape differences of the beam profile are covered, since the measured cross section depends on the shape of the interaction region. “Afterglow” effects are caused by late-arriving particles and activated material [183]. They induce a “ghost” response, even in unfilled runs, which has to be corrected for. The afterglow effect is negligible for a small number of bunches, but becomes significant if many bunches are combined in bunch trains [184].
The recorded integrated luminosity of the CMS experiment at√
s = 7 TeV is shown as a func-tion of time in fig. 3.16. Collisions corresponding to 6.13 fb−1were delivered to the CMS exper-iment in 2011, and the detector was fully operational to record data corresponding to 5.55 fb−1.
1 Apr 1 May 1 Jun 1 Jul 1 Aug 1 Sep 1 Oct Date (UTC)
0 1 2 3 4 5 6 7
Total Integrated Luminosity (fb¡1 )
Data included from 2011-03-13 17:00 to 2011-10-30 16:09 UTC LHC Delivered: 6.13 fb¡1
CMS Recorded: 5.55 fb¡1
0 1 2 3 4 5 6 7 CMS Integrated Luminosity, pp, 2011, ps = 7 TeV
Figure 3.16: Total integrated luminosity of proton-proton collisions at√
s = 7 TeV delivered to and recorded by the CMS experiment in 2011 [183].