This section will describe the different stages of the ATLAS particle flow algorithm in more de- tail [130].
4.3.1 Track-Cluster Matching
Reconstructed tracks constructed from hits in the ATLAS ID were extrapolated through the mag- netic field of the ID to the calorimeters; this provided the extrapolated impact coordinates of the tracks to different layers of the calorimeters. The extrapolated impact coordinates were then used to find the topo-cluster that was closest to the extrapolated track with the geometric variable D [130]:
D= v t (ηTrack− ηCluster)2 σ2 η + (φTrack− φCluster) 2 σ2 φ , (4.2)
where ηTrackand φTrackare the extrapolated η and φ track coordinates at the second layer of the EM
σηis the standard deviation of the η coordinates of all the cells within the topological cluster, and
σφis the standard deviation of the φ coordinates of the cells within the topological cluster. Using
the variance of the topo-cluster coordinates (σ2) means D takes into account the geometric size of
the topological cluster within the calorimeter; therefore, the track matching algorithm is not biased towards large calorimeter clusters.
If no track was matched to the topo-cluster, it remained unmodified and the measurements from the calorimeters were used. The particle flow algorithm treats the cluster as a neutral cluster made from a neutral particle. However, if tracks were matched to the cluster, then the cluster continued to the charged shower subtraction process.
4.3.2 Charged Shower Subtraction
Charged shower subtraction removes the energy deposited by the charged particle from the topo- cluster with the associated tracks. The amount of energy removed was determined by measuring the calorimeter response, E/P, where E is the energy of the cluster in the calorimeter and P is the momentum of the associated track. E/P was expected to vary depending on the region of the calorimeter (e.g. the ‘crack’ region (|η| ≈ 1.5) of the EM calorimeter) and the energy of the incident particle. Single pion MC samples of different energies were used to measure E/P in different bins of η and E to take into account changes of the calorimeter response. Another important parameter was the layer of first interaction: this was the layer of the calorimeter that the pion started to shower, and it also had the highest energy density. The layer of first interaction was found using the longitudinal energy density profile of the pion shower in the calorimeter. Energy was subtracted from calorimeter cells in the topo-cluster until the total amount of energy subtracted from the cluster was consistent with the fraction from the E/P distribution. This was performed in rings of calorimeter cells starting at the impact coordinates of the layer of first interaction [130].
It was possible for deposits from hadronic showers to split into different clusters between layers of the calorimeter (see Figure4.3); in this case, a split-shower recovery algorithm attempted to recover the other clusters associated with the charged pion. If the split-shower recovery did not recover all the cells from the hadronic particle, then there would be double counting of some of the energy
from the pion. In Figure4.3, some of the energy from the neutral pion would also be removed in
the main cluster, as the momentum of the charged pion track would be much greater than the energy of the charged fraction of the main cluster, and therefore the algorithm would continue to subtract energy from the main cluster until the total energy subtracted was consistent with the momentum of the track: this is the origin of the ‘confusion’ term, where neutral cell deposits are also removed by the algorithm.
Figure 4.3: An example schematic showing the splitting of a hadronic shower in the calorimeter
caused by a charged pion. The grey cells show the deposits from the π±, whereas the black cells
show the deposits from a π0. The right-hand part of the figure shows how the algorithm would treat
the cluster if the split-shower recovery method was not active, treating the other clusters from the π±as if they were made from a different neutral particle. This figure was taken from [130].
Figure 4.4: An example schematic showing the optimal outcome of the charged shower subtraction
algorithm. The grey cells show the deposits from the π±, whereas the black cells show the deposits
from a π0. The right-hand part of the figure shows how the cluster would look after the charged
After the charged shower subtraction process, only energy from neutral particles should be in the calorimeter cluster and the track momentum of charged particle associated with the cluster can be
used as the the charged fraction energy of the hadronic shower. This is shown in Figure4.4with all
the cells from the π±removed and only the cells from the π0remaining.
4.3.3 Calibration
The particle flow algorithm was performed before any of the topo-clusters were calibrated; this
meant the calorimeter deposits were at the EM scale (see section3.6.1). After the charged shower
subtraction process, only neutral deposits remained in the calorimeter; therefore, these clusters must now be fully calibrated to the appropriate energy scale. If they were not, then jets formed with the
remaining topo-clusters would not be properly calibrated (see section3.6.1).
4.3.4 Particle Flow Object List
Once the particle flow reconstruction algorithm was complete, a particle flow object list was created from all of the final reconstructed objects. This included all of the charged PFlow objects (tracks) and neutral PFlow objects (topo-clusters). However, not all of the tracks in the event would have
originated from the primary vertex, due to pile-up in the event (see section3.4). Therefore, a pile-
up track suppression cut is required. The pile-up track suppression cut compares the track impact
parameter (z0) to the z0 of the selected primary vertex. If the difference between the track impact
parameter and the primary vertex is greater than 2 mm, it is considered as a pile-up track, and was not included in the jet formation algorithm or the soft term of the ETmiss. This provides an inherent pile-up suppression built directly into the particle flow reconstruction algorithm, which should make reconstructed particle flow objects more robust to pile-up.