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Figure 4.11: Sketch of the workflow of the eflowRecalgorithm (from [111]).
energy deposits are subtracted from the calorimeter measurements to be left with the deposits of neutral particles, where the actual subtraction scheme can vary for different algorithms. In the following a short summary of the eflowRecalgorithm implemented in the ATLAS software framework is given. A more detailed description of this algorithm can be found in reference [111].
Figure 4.11 sketches the general workflow of eflowRec. eflowRec uses so-called topo-logical clusters built from the measurements in the calorimeter cells [81]. They cor-respond to spatially connected regions in the calorimeter, where the clusters can span the transverse direction within one calorimeter layer, but also longitudinally between different layers. Starting from seed cells above a certain energy threshold above the noise level of the calorimeter cell, surrounding cells are searched for until they fall below further energy thresholds. Different settings of the clusterisation have been investigated in the context of the tau reconstruction for PanTau as well [112], but the results will not be repeated here. Optimally one would have a one-to-one correspondence between calorimeter clusters and physical particles. In practice, however, a single topological cluster can contain showers from more than one particle and energy deposits of hadrons may be split into several clusters.
Reconstructed tracks are selected with very loose quality requirements and extrapo-lated into the second calorimeter layer. Here the nearest topological cluster in η and φ is selected, where the width of the clusters is taken into account. The energy Ecluster of
the matched cluster needs to fulfill the requirement
Ecluster> Eexpected−k2 ·σexpected (4.3) whereEexpectedis the expected energy deposition of a charged pion corresponding to the track andσexpected its uncertainty in order to make sure that the cluster does not have significantly less energy than one would expect. k2 is an additional parameter which needs to be tuned. If the condition is satisfied, the expected energy is removed from the cluster using a special subtraction scheme described later. The track together with its matched cluster forms a so-called chargedeflowObject(EFO), where the 4-momentum of the eflowObject is derived from the track information. This procedure is repeated for all other tracks matched to the cluster.
The energy-subtracted remnant cluster can still contain a certain amount of energy.
If the remaining energy exceeds the threshold
Ecluster0 > k1·σexpected (4.4)
one assumes that the energy is not simply a fluctuation in the energy deposition, but was caused by additional neutral particles in the same direction. Those remnant clusters and topological clusters without any matched track form neutral eflowObjects where the 4-momentum is calculated from the cluster applying a local calibration of the cluster energy using cluster shapes (local hadron calibration, [113]). If no cluster with the above requirement can be matched to a track a charged eflowObject without an assigned cluster is created.
Electromagnetic showers of electrons and photons in the calorimeter are usually very regular and can be well described by shower models. The interactions of hadrons in the calorimeter on the contrary can be very irregular, i.e. a single hadron may create several non-connected energy deposits. In this case the energy of the particle is split between those clusters and requirement (4.3) is not fulfilled. Without this requirement one would therefore double count part of the energy, because only one of the clusters would be matched to the track and the others would be interpreted as additional neutral clusters. If a track and a cluster have been matched, while the requirement is not fulfilled, eflowRec uses a conservative approach. It creates a charged eflowObjectwith assigned track and cluster, but the energy is calculated from the cluster. This way the total energy is kept constant and double counting of energy is avoided, even though one gives up the good momentum resolution.
The energy requirement alone does not fully solve the problem, though, because in the above example one would end up with a charged EFO having the energy of the cluster and several additional neutral EFOs. This effect can be seen in Figure 4.12a, where the energy resolution of the charged component of τ±→π±π0ν decays as reconstructed witheflowRecis shown. Obviously in a significant fraction of the tau decays the charged component is underestimated, while the neutral component is overestimated by the same amount. This has been fixed with the implementation of a recovery algorithm for split
(a) (b)
Reconstructed Charged ET/Visible Charged ET 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Number of Events
0 50 100 150 200 250 300
(a) without splitting recovery
(a) (b)
Reconstructed Charged ET/Visible Charged ET 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Number of Events
0 100 200 300 400 500 600
(b) with splitting recovery
Figure 4.12: Energy resolution of the charged component of τ±→π±π0ν decays without (a) and with (b) recovery of the cluster splitting (from [111]).
clusters. The recovery searches for compatible clusters within a ∆R < 0.2 cone around the extrapolated track path through the calorimeter. Afterwards the track energy is subtracted from all those clusters using the same subtraction procedure as before. The impact of the Split Shower Recovery algorithm can be seen in Figure 4.12b, where nearly all decays with significant underestimation of the charged component could be corrected.
One of the most important points, where energy flow algorithms differ is the way how the estimated energy of the extrapolated track is subtracted from the calorimeter clusters. eflowRec uses a cell ordered subtraction,i.e.one first defines a cell ordering and afterwards subtracts the contribution of each cell to the cluster until the expected energy of the track has been fully subtracted. The idea behind this approach is motivated by the properties of hadronic showers in the calorimeter (cf. [8] and references therein).
At the position of the first interaction a prompt electromagnetic shower is created from the production of neutral pions decaying into photons. The photon induced showers create a core with high energy density. They are surrounded by a more diffuse shower of additional hadronic interactions creating a long tail in the energy distribution of the full shower. Therefore it seems natural to subtract the core first as it has the highest energy density and the more regular shape.
In the cell ordering the energy density per cell is weighted by the distance from the extrapolated track position using a two-dimensional Gaussian distribution with a width of 3.5 cm, approximating the Moli`ere radius. Together with an estimate of the position of the first interaction of the shower one can derive “rings” around the extrapolated track in which the cells are ordered. Parametrisations of the mean radial shower profile allow to estimate the relative energy fraction expected to be deposited in each ring in the different calorimeter layers. This information is used to determine the ordering by energy density, but not to estimate the amount of energy to be subtracted.
eflowRec finally provides a collection of charged and neutral energy flow objects (EFO). They also include information on the cluster shape in the calorimeter allow-ing for a distinction between clusters from hadrons and electrons/photons. The energy flow objects are intended to yield a consistent picture of charged and neutral particles in the detector, while using the best knowledge from the tracking system and the calorime-try. They can be usede.g.to calculate the missing transverse energyETmiss or – as in the case of PanTau– to reconstruct and identify jets from hadronic decays of tau leptons.