Muon reconstruction is very robust and efficient, attributable to several redundant and accurate layers of detection [67]. As explained in chapter 6, a DT chamber reconstructs a linear segment of the muon track. Similarly, CSC build linear segments from the 6 planes of reconstructed 2-D hits.
Then, segments are extrapolated from one DT or CSC to the next station, using a Kalmar Filter. The magnetic field, the multiple scattering inside the steel yoke, and the energy loses are taking into account. A standalone muon track is reconstructed in the muon system.
The last step of reconstruction is the matching of the standalone track with a track in the inner silicon detector. Two types of muons are considered, according to their reconstruction process:
• Global muon: The standalone track is extrapolated to the tracker and a search is performed in a cone around it to match a tracker track.
• Tracker muon: All tracker tracks with transverse momentum pT>0.5 GeV are considered as seeds and extrapolated to the muon system, looking for a match with a DT/CSC segment.
A tracker muon is less restrictive in the muon system reconstruction (only requires a muon segment) so it will be slightly more efficient for low-pT muons, which might not cross enough muon stations as to reconstruct a standalone track. However, over pT>5 GeV, differences in efficiency are negligible. In fact, more than 99% muons in the detector acceptance are reconstructed by both methods.
Different analyses in CMS may need different commitments between efficiency and purity in the identification of a muon. Several quantities are used to classify identified muons in different types according to their purity: loose, soft and tight muons. These quantities cover:
• quality of the tracker track: to guarantee a good pT measurement.
• thresholds in the impact parameter of the track: to suppress muons created in decays in-flight of hadrons (e.g. muons coming from b,c decays) and cosmic rays. • χ2 cut of the track fit and requirements in muon system: to further suppress
muons from decays in-flight and punch-through.
Table 7.1 summarizes the selection criteria for muons with different level of purity. Loose muon category is skipped as it only requires a muon to be a PF muon with a global or tracker track. Furthermore, an additional selection is dedicated to high-pt muons (over 200 GeV) which is useful in certain analyses.
The purity varies from a 7% of punch-through and fake muon contamination in soft muons, to less than 0.5% in tight muons.
7.1. Muons 91
Soft Tight
Tracker track global track
- PF muon
tracker layers w. hits >5 tracker layers w. hits >5
pixel layers w hit >1 Valid pixel hits >0
χ2/n.d.o.f. of tracker track fit <1.8 χ2/n.d.o.f. of global track fit <10
Loose IP cuts Tight IP cuts
- muon chambers in fit >1
- muon hits in global track >0
Table 7.1: Requirements on muon identification with different level of efficiency and purity.
The ”tag & probe” method provides an almost unbiased estimation of the efficiency of muon trigger and offline reconstruction. This method uses dimuon resonances (J/ψ to study the low pT regime, Z for the intermediate one) and tags one of the muons with the full selection criteria. The efficiency is evaluated on other muon, (probe), subject to different selection criteria depending on the efficiency to measure.
The full efficiency of a reconstructed muon is expressed as the convolution of several efficiencies:
µ= tracking× RECO+ID× ISO × trigger (7.1)
where tracking is the efficiency of the track reconstruction of the inner tracker, RECO+ID is the efficiency of reconstructing and identifying a muon, ISO is the efficiency of the isolation criteria (described below) and trigger is the efficiency of the muon trigger system. tracking is more than 99% within the tracker acceptance. The RECO+ID is (99±0.24%) for soft muons and more than 96% for tight muons (96.4±0.2% in the barrel and 96.0±0.3% in the endcaps), in excellent agreement with simulation.
The muon trigger efficiency is also evaluated with the tag&probe method from dimuon resonance samples. The efficiency depends on the kinematics of the muon and the purity of the identified muon. Most of the inefficiency is due to pT thresholds in the L1 and HLT algorithms (which affects the very low pT regime) and due to inefficiency in the barrel-endcap overlap region. For tight muons, a plateau efficiency is reached for pT over 10 GeV, of ∼ 95 % in the central region.
7.1.1
Isolation
The study of the activity of the detector in the vicinity of a muon track allows the discrimination between a muon coming from the decay of a weak boson and and a leptonic decay of an hadron, especially those that contain a heavy-flavour quark. The criteria of isolation is established as a certain threshold on the ratio of the sum of pT of objects reconstructed in a cone around the muon itself to the muon pT. This
sum of pT in the numerator may be based on detector information, using tracker tracks (tracker isolation) or tracker tracks and energies measured in ECAL and HCAL towers (combined isolation). PF relative isolation, in contrast, uses particle-flow reconstructed particles: charged hadrons and transverse energies ET of all photons and neutral hadrons.
The cone is defined by its radius ∆R ≡p(∆φ)2+ (∆η)2, optimized independently for the different algorithms.
Figure 7.2 shows the efficiency of the isolation criteria as a function of the pT for the combined tracker+calorimeter algorithm (left) and particle-flow algorithm (right). The thresholds in each case are decided representing the efficiency of the isolation as a function of the value of the threshold, and picking the value where the efficiency reaches a plateau.
Figure 7.2: Left: efficiency of tracker-plus-calorimeters relative isolation for muons from Z decays as a function of muon pT. Results corresponding to the threshold values
of 0.10 and 0.15 are shown. Right: efficiency of particle-flow relative isolation for muons from Z decays as a function of muon pT. Results corresponding to the threshold values
of 0.12 and 0.20 are shown.
Pileup has a strong effect in the isolation determination. The amount of energy collected in the cone around the muon candidate rises and the isolation decision is biased. The increase of the luminosity in the LHC enforces to develop techniques to remove the pile-up contribution to the amount of energy measured. The pile-up charged particle contribution is easily identified due to the good vertex resolution, but the neutral particle contribution needs further corrections. In the effective areas correction, an average pile-up energy density ρ is calculated per event, based on the FastJet reconstruction algorithm [77]. The neutral contribution in the cone is thereby corrected as X n.c pt → max 0, X n.c pT − ρ · Aef f ! (7.2)