Cell Clustering Algorithm

N_φ^window is 3 ×5. The position of the precluster is calculated by the energy weighted η and φbarycenters of all cells within a fixed size window around the tower at the center of the sliding window. If two preclusters have their positions within a distance (∆η×∆φ), the precluster with the larger transverse energy is remained and the other precluster is removed. The filling procedure for EM cells is complex. The algorithm considers all cells within a rectangle of sizeN_η^cluster×N_φ^cluster centred on a layer-dependent seed position. Table 4.3 show the parameters of the precluster finding for EM in the window algorithm. The order indicates the processed order of each layer. The layer indicates the name of the layers. The middle is the second layer of EM calorimeter. The strip is the first layer of EM calorimeter. The back is the third layer of EM calorimeter. ∆η_cl and∆φ_cl indicates the size of the cluster filled with the cells around the seed position.N_η^clusterandN_φ^cluster changes for different particles as shown in Table 4.4. ∗means that either one or two cells in φ of size 0.1 are used if the cluster sizeN_φ^window is less than seven. The seed position indicates the layer-dependent seed position.

Table 4.3: Parameters of the precluster finding for the EM calorimeter in the window algorithm.

Order Layer ∆η_cl(units of 0.25) ∆φ_cl(units of 0.25) Seed position

1 Middle N_η^cluster N_φ^cluster η_precl, φ_precl

2 Strips N_η^cluster 6 or8^∗ η_middle, φ_middle

3 Presampler N_η^cluster 6 or8^∗ η_strips, φ_strips 4 Back N_η^cluster+ 1 N_φ^cluster η_middle, φ_middle

Table 4.4: Cluster size N_η^cluster ×N_φ^cluster for different particle types in the barrel and end-cap regions.

Particle Type Barrel Endcap

Electron 3×7 5×5

Converted photon 3×7 5×5 Unconverted photon 3×5 5×5

The algorithm runs on the middle layer of electromagnetic calorimeter first. The seed position in the middle layer is the precluster barycenter positionη_precl, φ_precldetermined in the precluster finding which uses total layer information. The barycenter η_middle, φ_middle is calculated by the cells in the middle layer. Second, the strip layer uses theηmiddle, φmiddleas the seed position. The barycenterη_strips, φ_stripsis calculated by the cells in the strip layer. Then, the algorithm performs the cluster filling for the presampler layer and back layer by using the barycenterη_strips, φ_stripsand η_middle, φ_middle. In Table 4.4, the larger value ofφindicates the effect from the magnetic field.

Next, we refer to the topological clustering algorithm. The algorithm consists of two steps; the cluster maker, the cluster splitter. In the cluster maker, the algorithm forms topological clusters from a list of calorimeter cells. In the cluster splitter, the algorithm can splits individual clusters, which originate from different showers, but are overlapped. The cluster maker performs the fol-lowing procedures; finding seeds, finding neighbors, finalize. Table 4.5 show parameters used to build the two types of topological cluster available in the standard ATLAS reconstruction. We use the Had420 parameters. The details of the parameters is described below.

• Finding seed: The algorithm finds all cells with a signal to noise ratio above the seed thresh-oldt_seed. Then, it makes the list of the seed cells, which form proto-clusters. The signal employed for the threshold comparison can either be the cell energy or its absolute value.

We employ the absolute value for finding seeds in the jet reconstruction. The noise consists of the electronic component and the pile-up component where they are combined by the square root of sum of suares. In 2010 operations, we considered the electronic component only due to the low interaction rate. After 2011 operations, we consider both components.

Their contributions to the calorimeters are studied by using the simulation data [106]. Fig-ure 4.6 shows the noise distributions for the 2010 operations, which are evaluated by using the MC simulation with the average ofpp collisions per bunch crossing ofµ = 0and the center of mass collision energy of 7 TeV. Figure 4.7 shows the noise distributions for the 2011 operations, which are evaluated by using the MC simulation with the average ofpp collisions per bunch crossing ofµ= 8and the center of mass collision energy of 7 TeV. The different colour plots indicate the different type of calorimeters and layers. PS is the pre-sampler in front of the EM calorimeter. Gap is the scintillators installed in the gap between cryostats. In the region of|η|>2.5, the contribution from the pile-up component is visible in Figure 4.7.

Figure 4.6: Noise distributions for the 2010 oper-ations are evaluated by using the MC simulation with the average ofppcollisions per bunch cross-ing of µ = 0 and the center of mass collision energy of 7 TeV. The distribution is shown as a function of|η|. The different colours indicate the different type of the calorimeters and layers.

Figure 4.7: Noise distributions for the 2011 oper-ations are evaluated by using the MC simulation with the average ofppcollisions per bunch cross-ing of µ = 8 and the center of mass collision energy of 7 TeV. The distribution is shown as a function of|η|. The different colours indicate the different type of the calorimeters and layers.

• Finding neighbors: All cells in the seed list are ordered in descending order in signal to noise ratio. For each seed cell in turn, the algorithm checks the neighboring cells. If a neighboring cell has not been used as a seed so far, and its signal to noise ratio is above the neighbor thresholdt_neighbor, the cell is added to a neighboring seed list and included in the adjacent proto-cluster. If the neighboring cell is adjacent to more than one proto-cluster, the proto-clusters and the cell are merged. If a neighboring cell has the signal to noise ratio, which is above the cell thresholdt_cell but belowt_neighbor, the cell is added only to the first adjacent proto-cluster, which is the one providing the more significant neighbor to this cell. Once all seed cells have been processed, the original seed list is discarded and the

neighboring seed list becomes the new seed list. This procedure is repeated until the seed list is empty.

• Finalize: The remaining proto-clusters are sorted in descending order inE_Tand converted to clusters. The algorithm removes the converted clusters withET less than a threshold for cluster cut before splitting.

The cells in a single calorimeter layer or the cells from adjacent layers and subsystem are utilized as neighboring cells. The EM633 can be used to reconstruct EM clusters significantly higher than the noise with minimum fake rate. The Had426 is optimized to find efficiently low energy clusters without being overwhelmed by noise.

Table 4.5: Parameters used to build two types of the topological cluster available in the standard ATLAS reconstruction.

Parameter EM633 Had420

Calorimeters EM All

Seed signal definition E |E|

Cluster cut before splitting E_T>5GeV |E_T|>5GeV

t_seed 6 4

t_neighbor 3 2

t_cell 3 0

The cluster splitting is used for separating the clusters of showers from the clusters of particles passing close to the shower. The splitting performs the following procedures; finding local max-ima, finding neighbors, shared cells and finalize as follows:

• Finding local maxima: The algorithm searches for local maximum cells in clustered cells defined as follows.

– a cell hasE >500MeV.

– Its energy is greater than energies of any neighboring cells.

– A number of neighboring cells within the parent cluster is above a threshold.

The algorithm forms a list of local maxima once, the number of final clusters is completely determined. This indicates that each local maximum cluster will form exactly one cluster and the parent clusters without any local maximum cell will not be split.

• Finding neighbors: The algorithm adds the cells, which are adjacent to the local maxima, to the maximum cells. There is no thresholds for adding the cells and no cluster merging.

The local maxima list serves as the initial seed list. At each iteration, the current seed list is sorted in descending order in energy. All cells, which are not used in the adding procedure but directly neighbor to the seed cells, are added to a neighboring seed list and included in adjacent clusters. If a cell neighbors to more than one cluster, the two proto-clusters with the most energetic neighbors will share the cell. The shared cells are removed from the neighbor list, then they are added to a shared cell list. Once all seed cells are processed, the original seed list is discarded and the neighboring seed list becomes the new seed list. This procedure is repeated until the seed list is empty.

• Shared cells: The algorithm iteratively adds the neighbors, which have not been assigned to any proto-cluster yet but belong to the original cell set, to the shared cell list. The algorithm associates these cells with the two proto-clusters adjoining the original shared cell that they neighbor. Each cell in the expanded shared cell list is added to its two adjoining proto-clusters with the weights expressed by

w₁ = E₁

E₁+rE₂, w₂ = 1−w₁, r = exp(d₁−d₂), (4.15) whereE_1,2are the energies of the two proto-clusters andd_1,2are the distance of the shared cell to the proto-cluster centroids in units of a typical EM-shower scale.

• Finalize: The algorithm adds all parent clusters without a local maximum to the list of proto-clusters. The cluster list is sorted in descending order inE_T. Finally, the all listed proto-clusters are converted to clusters.