Muon Reconstruction

The muon trigger efficiency has been determined from data in minimum bias events. The statistical uncertainty on the trigger efficiency amounts to 3-5%, depending on the muon transverse momentum and pseudorapidity, and is taken as a systematic uncertainty. The muon reconstruction efficiency is known to a precision of 3%. The tracking efficiency for hadrons is known with a precision of 4%. This induces a systematic uncertainty of 2% on the number of events passing the event selection. The uncertainty in the tracking efficiency affects the b-fraction in the fit by about 1%. 

Muon reconstruction, after local-pattern recognition is performed in two stages stand-alone reconstruction based on information from the muon system only and global reconstmction including the hit information of the silicon tracker. Standalone reconstruction starts from track segments in the muon chambers and muon trajectories are built from the inside to the outside using the Kalman filter technique. After the trajectory is built, a second Kalman filter, working from outside in, is applied to determine the track parameters. In the end, the track is extrapolated to the nominal interaction point and a vertex-constrained fit of the track parameters is performed. 

Figure 2. Detection principle of an underwater neutrino telescope. Astrophysical neutrinos can reach the Earth and interact in water or in rocks generating an upgoing muon. An array of 5000 optical detectors tracks Cerenkov photons generated along the muon track. A water shielding > 3000 m is effective to reduce the atmospheric fi background, allowing the reconstruction of upgoing muon tracks.

The space-time pattern of Cerenkov wavefront can be reconstructed during off-line analysis fitting relation 9. The reconstructed muon direction will be affected by indetermination on PMTs position (due to underwater position monitoring) and on hit time (PMT transit time spread, detector timing calibration,...). 

Figure 5 Mean logarithmic mass of cosmic rays reconstructed from a) experiments measuring electrons, muons, and hadrons at...

Figure 3. Uncertainties in reconstruction Figure 4. Reconstructed muon size spectrum of total muon number...

Fig. 1. I i>ical muon event recorded with the l/2mxl/2m prototype drift chambers with 90% Xe and 10 % methane at 1 atm. The crosses indicate the position of the anodes which are separated by 4 cm. Each horizontal row of anodes constitutes a frame which is 1 cm high, and the total stack height is 50 cm. Half of the frames are offset by half a drift cell to eliminate the left/right ambiguity. The triangles are the hit positions corresponding to left or right drift towards the anode. The numbers on the right hand side are residuals in units of mm for each point used in the reconstruction.

Even though the CMS detector is primarily designed for high transverse momentum physics, it is very well suited for heavy flavor physics thanks to the muon system with the potential to identify low transverse momentum muons and the excellent tracking detectors. In particular, CMS features a novel three-layer silicon pixel detector which allows for a precise and efficient reconstruction of secondary vertices from heavy flavor decays. 

Fig. 4.10 Simulated distribution of reconstructed muon transverse momentum and pseudorapidity in signal events passing the event selection. The distributions are normalized to an integrated luminosity of lpb ...

As discussed in the previous section, the first requirement of the event selection is a reconstructed muon with transverse momentum pr > 5 GeV and pseudorapidity —2.1 < T] < 2.1. Only global muons, i.e. muons identified in the tracking detectors as well as in the muon chambers, pass the selection. If more than one muon is present in the event, the muon with the highest transverse momentum is chosen. The transverse momentum and pseudorapidity distributions of muons passing the event selection are shown in Fig. 4.10 for fe-events. 

The assignment between the reconstructed muon and the TrackJet is based on the result of the TrackJet clustering algorithm. The muon is associated to a TrackJet if the muon track lies within the TrackJet with transverse energy 7- > 1 Gev. The... 

Fig. 4.11 Distance between the reconstructed muon and the TrackJet (A/f) for selected...

Fig. 4.12 Fraction of h-events in the inclusive sample as a function of the transverse momentum and the pseudorapidity of the reconstructed muon...

The differential fc-quark production cross-section is measured as a function of muon transverse momentum and pseudorapidity. The flavor composition is determined by performing a fit in each analysis bin. The binning is chosen such that the number of events in every bin is sufficient for a stable fit and at the same time a maximum purity is achieved. The purity V is defined as the fraction of selected reconstructed events in each bin that have the respective generated quantity in the same bin and is calculated based on the MC simulation ... 

Here NrJf is the number of reconstructed MC events with muon transverse momentum (or pseudorapidity) in bin i. The reconstrutced muons are matched to generated muons (based on Ai ) in order to determine N fJ Sgen i.e. the number of events with both reconstructed and generated muon transverse momentum (pseudorapidity) in bin i. The purity takes into account bin-to-bin migration caused by resolution effects and contributions from fake muons in ( -events. 

Tracks from the underlying event can change the properties of TrackJets associated to the muon. Especially in events with low multiplicity TrackJets, the distribution of additional tracks may influence the TrackJet reconstruction efficiency and angular... 

Within the analysis presented here the events of interest are selected by requiring a global muon with transverse momentum pr > 5GeV and pseudorapidity t) < 2.1 and a TrackJet with transverse energy Ej > GeV in the reconstructed event. 

In the first section the event selection is discussed, before an overview of the event simulation is given. The following sections are devoted to the global muon, track and TrackJet reconstruction. A further section addresses the determination of the variable in data. The conclusions are given in the last section. 

In Fig. 5.4 the number of tracks reconstructed within a TrackJet and the transverse momentum of the highest transverse momentum track are compared to the MC simulation and a good agreement is found. These results are relevant in view of the measurement of the -quark production cross-section as the analysis presented here is based on a precise determination of the muon momentum with respect to the TrackJet direction. A good understanding of the TrackJet reconstruction and a reliable simulation of the TrackJet distributions are thus of utmost importance. 

The data recorded during the first collisions in December 2009 have been used to study the performance of the physics object reconstruction. The number of global muons in the collision data is very small. However, the reconstruction of global muons was already well commissioned using cosmic data. The reconstruction of tracks and TrackJet was studied and a in general the data were found to be well described by simulation. This result is most valuable in view of the analysis presented in this thesis. 

The CMS data are compared to the PYTHIA MC simulation version 6.4 with tune D6T. For simulation and reconstruction the CMS software version CMSSW 3 5 X was used. Two statistically independent samples were generated an inclusive QCD minimum bias sample and a muon-enriched QCD sample, in which the presence of a generated muon with pr > 2.5GeV and < 2.5 was required (compare to Sect. 4.2). An overview of theMC simulation is given in Table 6.1. 

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