where Aef f is an effective area of the cone, calculated to remove the dependency on the number of reconstructed primary vertices.
An equivalent method has been developed called delta beta corrections (∆β) computes the pile-up charged particle deposits produced in other vertices, and estimates the neutral counterpart from an average charged/neutral particle established ratio.
7.1.2
Momentum scale and resolution
The measurement of the muon transverse momentum is strongly dependent of the alignment of the tracker and the muon system, and the knowledge of the magnetic field and of the energy loss in all the volume of the detector.
Tracker resolution dominates the muon momentum resolution. Only for high- pT muons, the global muon fit improves the momentum resolution with respect to the tracker fit. The default algorithm for momentum assignment estimates the tracker-only fit momentum and the global-fit momentum. Then, the global fit is chosen when both fits yield a muon pT above 200 GeV and give the charge-to-momentum ratios q/p that agree to within 2σq/p of the tracker-only fit; in all other cases the tracker-only fit is taken.
Muon momentum scale is calibrated using the mass constraint in dimuon decays of J/ψ and Z resonances, at low and intermediate pT range, respectively. For pT larger than 100 GeV, cosmic-ray muons are used (except in the region of high pseudorapidity). In this case, the ”Tune P ” algorithm, which takes into account possible radiation losses in the material, is used to improve the pT resolution.
Muon momentum resolution is also evaluated with J/ψ and Z resonances and cosmic rays, smearing simulation to match data. Resolution depends on the pT and the region of the detector.
At low and intermediate pT, the resolution σ(pT)/pT depends on the pT of the muon and the region of detection. Figure 7.3 (right plot), shows the dependence of the resolution of a tight muon with η. The dependence on pT, on average, varies from 1.8% for at pT=30 GeV to 2.3% at pT=50 GeV.
Resolution q/pT for high-pT muons, over 200 GeV, measured with cosmic rays, is shown in Fig.7.3 (left plot), for different algorithms.
In conclusion, the specifications of σ(pT)/pT ∼ 1% at 100 GeV and σ(pT)/pT ∼ 10% at 1 TeV are satisfied.
7.2
Electrons
The reconstruction of electrons is done together by the ECAL and the tracker detector. One critical aspect is the big amount of silicon material the electrons have to traverse, which induces big losses through bremsstrahlung photon radiation. High energy electromagnetic showers spread laterally over several crystals, so the reconstruction starts with ”hot” crystals in the ECAL being grouped in clusters. To
Figure 7.3: Left: Widths of Gaussian fits of the distributions of the muon q/pT relative
residuals as a function of the pT of the muon, for different reconstruction algorithms:
tracker-only and global fits, and the output of the sigma-switch and Tune P algorithms. Right: Relative transverse momentum resolution σ(pT)/pT in data and simulation for
muons of pT∼ 50 GeV.
recover radiation from bremsstrahlung losses and conversion of photons from electrons, clusters are grouped along the φ coordinate in superclusters. Because of the different geometry of the detector in barrel and endcap, different clustering algorithms are used in different regions [78]. Superclusters are used as seeds to find hits in the pixel detector. The track is built with a Kalman Filter. The Gaussian Sum Fitter (GSF) algorithm is used to refit and re-estimate the inner track (reconstructed with the tracker) taking into account the bremsstrahlung losses.
The final identification is based in different detector variables, which may be used independently with optimized thresholds for each one (cut-based identification), or combined with some multi-variate analyses technique (MVA identification).
• ∆η(SC, ~p(vtx)): η separation between the ECAL supercluster position and the track direction in the vertex, extrapolated to the ECAL, assuming no radiation. • ∆φ(SC, ~p(vtx)): φ separation between the ECAL supercluster position and the track direction in the vertex, extrapolated to the ECAL, assuming no radiation. • EHCAL/EECAL: ratio of energy collected in the HCAL tower behind the ECAL weighted position of the ECAL supercluster, to the ECAL supercluster deposit, used to suppress hadronic jets misidentified as electrons.
• σiη,iη: width of the ECAL supercluster along the direction computed for all the crystals in the 5x5 blocks of crystals centred on the highest energy crystal of the seed supercluster.
7.2. Electrons 95
• dxy,dz: transverse and longitudinal impact parameter of the track, with respect to the reconstructed vertex.
• 1/Etot − 1/p : E is the energy measured in the ECAL and p is the momentum measured in the tracker at the vertex position.
• The number of missing hits in the back-propagation of the track to the beam line.
Reconstructed electrons from converted photons in the tracker are a non-negligible background to ”prompt” electrons at hadron collisions (e.g. electrons originated in the primary interaction point, like those from W and Z boson decays). Therefore, efficient methods to identify and reject such electrons are fundamental to any analyses that involves ”prompt” electrons, such as check missing expected hits in front of the innermost tracker layers.
Different working points are established, as for the muons, depending on the commitment between efficiency and purity of the identification [79]. Table 7.2 shows the full identification criteria for the Loose Working Point, representing an overall efficiency above 90%. Figure 7.4 shows the efficiency as a function of the pT for the Medium Working Point, which has tighter requirements, in two different acceptance areas.
The electron isolation is performed as explained in section 7.1 for muons. Effective area corrections are also applied to correct pile-up contributions.
Endcaps Barrel ∆η(SC, ~p(vtx)) <0.009 <0.007 ∆φ(SC, ~p(vtx)) <0.1 <0.15 σiη,iη <0.03 <0.01 EHCAL/EECAL <0.1 <0.12 dxy (cms) <0.02 <0.02 dz (cm) <0.2 <0.2 1/Etot− 1/p <0.05 <0.05 Missing Hits <=1 <=1
Conversion vertex fit prob. <10−6 <10−6
Table 7.2: Electron identification cuts for the Loose Working Point.
As for the case of muons, the electron energy scale is calibrated using the tag&probe method using Z → e−e+samples. Additional corrections or smearings are applied to the simulation to account for possible differences with respect to the data reconstruction. The energy resolution is also evaluated with this tag&probe method, splitting the sample according to the amount of bremsstrahlung losses, in order to exploit calorimetric or tracker variables. Furthermore, it is significantly improved using multivariate regression techniques.
Figure 7.4: Electron selection efficiency for the medium working point (WP) on data and on a Drell-Yan Monte Carlo simulation sample as a function of the electron pT, for two η regions: 0 < η < 0.8 (left) and 2.0 < η < 2.5 (right). Only statistical errors are shown.
Figure 7.5 shows the measured resolution in data an simulation for different categories in Z → e−e+resonances [79]. The resolution in the barrel is in 1-2.5%, whereas in the endcaps rises to near 3-4%, depending on the category.