Detector reconstruction and performance

6.4 Detector reconstruction and performance

6.4.1 Tracker

Tracks are reconstructed from the hits in the tracker using an iterative algorithm called the Combinatorial Track Finder (CTF) [182], based on the Kalman filter [187]. CTF starts by finding the “easiest” tracks (e.g. of high $p_{T}$ and produced near the interaction region), removes their hits from the search, and then repeats the process until all tracks have been found. Due to the high computational cost of track reconstruction, this cannot be performed at the L1 trigger and, hence, track information is not used for the L1 trigger decision currently in CMS.

Offline, CMS is able to reconstruct isolated muons of $p_{T} > 0.9 GeV$ with 100% efficiency within the tracker acceptance of $| η | < 2.4$ , with a $p_{T}$ resolution of up to $2.8 %$ for $p_{T} \sim 100 GeV$ [182]. The pixel tracker can also achieve a vertex position resolution of $10$ – $12$ $μ m$ in all three spatial dimensions. $B$ -hadrons produced in the $pp$ collisions generally travel on the order of a few millimeters before decaying and, hence, the precise vertexing of the CMS tracker allows for efficient $b$ -tagging [188] and even boosted $bb$ -tagging [164], as is crucial for the analysis described in this dissertation.

6.4.2 ECAL

Signals in the ECAL crystals are reconstructed by fitting the signal pulse with template pulse shapes to distinguish OOT pileup, both offline and online [183]. The individual hits are then clustered to identify electromagnetic showers initiated by the same incident particle, and are further clustered into “superclusters” to account for photon conversions and bremsstrahlung losses [189]. Clusters are tested for compatibility with reconstructed tracks from both single electrons and pair-produced electrons by photons, and the combined information is used to identify electrons and photons. Cluster energies are calibrated based on differences in neutral pion to two-photon decays in data and simulation [48].

With the PF algorithm, electrons (isolated photons) are identified by the ECAL clusters, the presence (absence) of a corresponding track in the tracker, and a low relative energy deposit in the HCAL along the particle trajectory. The online triggers use a similar but simplified algorithm with tighter requirements on electron and photon identification. Offline, multivariate regression algorithms are used to correct the raw measured energy for inefficiencies due to energy loss before or in the ECAL.

Overall, the ECAL has been measured in data collected by CMS to have a reconstruction efficiency of > $95 %$ for $10 < E_{T} < 500 GeV$ , with an uncertainty on the electron and photon energy scale of $0.1 %$ in the barrel and $0.3 %$ , in the endcaps [189]. Electron energy resolution was measured to be between $2$ – $5 %$ in $Z \to e^{+} e^{-}$ decays.

6.4.3 HCAL

The energy of hits in the HCAL is estimated, and OOT PU rejected, by fitting pulse templates to the photodetector signals, both online and offline [190]. Corrections are applied as well based on measured reduction of the light output of the scintillators due to radiation damage and decrease in the photodetector efficiencies [191]. As the HCAL is a sampling calorimeter, the measured energy must be scaled to estimate the total energy of the hadronic shower. This scale factor is nonlinear with the energy of the incident particle, and is estimated through a variety of techniques using simulations and data for the different HCAL components and regions [191]. The overall energy scale is measured to a precision of < $2 %$ in the HB and HE, and < $3 %$ for the HO and HF.

A similar clustering algorithm to the ECAL’s is used in all HCAL subdetectors, with the exception of the HF where a hit in a cell is directly considered a “cluster’. As hadrons deposit energy in the ECAL as well, cluster energies in both calorimeters are calibrated together for hadrons, using a sample of neutral kaons [48]. As for electrons and photons in the ECAL, the PF algorithm is used to identify hadrons based on a higher relative energy deposit in the HCAL versus ECAL, and, for the case of charged hadrons, a matching track in the tracker.

Figure 6.14 shows the response — the relative mean difference between the measured and true energy of a particle — and resolution for single neutral hadron energies in the barrel as a function of the true energy, before and after calibration. We see that the energy resolution is significantly worse than for charged particles and photons — >10% for all energies — due to the modest resolution of the HCAL compared to the tracker and ECAL. However, neutral hadrons on average comprise only 10% of event and jet energies (the rest coming from 65% charged hadrons and 25% photons), which means the overall contribution is at the percent level.

Figure 6.14. Response and resolution of single neutral hadron energies in the barrel as a function of the true energy, before and after calibration, reproduced from Ref. [48].

6.4.4 Muon system

The muon system is triggered using the independent and complementary timing information from the DTs and CSCs in the barrel and endcap, respectively, and the RPCs in both. Hits are first reconstructed locally based on the timing information from the RPCs and the position and timing information from the DTs and CSCs. Hits along the muon chambers are then combined to form standalone-muon tracks using a Kalman filter technique [187]. Additional tracker muon tracks and global muon tracks are formed by propagating tracker tracks to loosely matched DT or CSC hits, and matching the standalone-muon tracks to tracker tracks, respectively [47]. The combined track information is used by the global PF algorithm to optimize muon identification and determine their momenta [48].

Overall, the muon reconstruction and identification efficiency has been measured to be > $96 %$ [47]. For lower $p_{T}$ muons ( $p_{T} < 200 GeV$ ), the momentum measurement is dominated by the inner tracker performance, with a resolution of approximately $1 %$ in the barrel and $3 %$ in the endcaps. For higher $p_{T}$ muons, the combined tracker and muon system information is important, with a measured resolution of < $6 %$ at $p_{T} \sim 1 TeV$ .

6.4.5 Object reconstruction and particle flow

The PF algorithm [48] is used to reconstruct and identify each individual particle in an event, with an optimized combination of information from the different subdetectors. The energy of photons is obtained from the ECAL measurement. The energy of electrons is determined from a combination of the electron momentum at the primary interaction vertex as determined by the tracker, the energy of the corresponding ECAL cluster, and the energy sum of all bremsstrahlung photons spatially compatible with originating from the electron track. The energy of muons is obtained from the curvature of the corresponding track. The energy of charged hadrons is determined from a combination of their momentum measured in the tracker and the matching ECAL and HCAL energy deposits, corrected for the response function of the calorimeters to hadronic showers. Finally, the energy of neutral hadrons is obtained from the corresponding corrected ECAL and HCAL energies. The primary vertex (PV) is taken to be the vertex corresponding to the hardest scattering in the event, evaluated using tracking information alone, as described in Ref. [192].

For each event, hadronic jets are clustered from these reconstructed particles using the infrared and collinear safe anti- $k_{T}$ algorithm [193, 194] with a distance parameter of 0.4 (AK4 jets) or 0.8 (AK8 jets). Jet momentum is determined as the vectorial sum of all particle momenta in the jet, and is found from simulation to be, on average, within 5 to 10% of the true momentum over the whole $p_{T}$ spectrum and detector acceptance. For the analysis described in this dissertation, the charged-hadron subtraction [195] and pileup per particle identification [196, 197] algorithms are used to mitigate the effect of pileup on AK4 and AK8 jets, respectively, and further corrections are applied to their energy and mass scales and resolutions to correct for detector mismodeling.

Electrons falling within the tracker acceptance are reconstructed using momentum derived from the tracker, the energy from the corresponding ECAL cluster, and the collective energy of all bremsstrahlung photons spatially aligned with the electron track [198]. Muons falling within the muon chamber acceptance $| η | < 2.4$ are reconstructed as tracks in the central tracker which align with tracks or hits in the muon chambers [47]. For the analysis described in this dissertation, electron candidates are required to fall within the tracker acceptance of $| η | < 2.5$ and have $p_{T} > 20 GeV$ , while muon candidates are required to be within the muon chamber acceptance of $| η | < 2.4$ and have $p_{T} > 10 GeV$ . Both leptons are then required to pass additional identification criteria [47, 198] to improve purity and be isolated [48] to suppress those originating from bottom or charm hadron decays.