Clustering algorithm

Clustering Effeciency

In the quick simulator, following algorithm is used to clusterize hit cell information of elemag calorimeter. Note that for hadron calorimeter, another algorithm for track-cluster matching developed by Keisuke Fujii is used without clustering of calorimeter's hit cell..

1.

Find highest energy counter BL1 whose energy larger than ETH.

2.

Find neighbor counter BL2 and include in the cluster.

3.

Find BL3 that is neighbour counter of BL2, include in the cluster if one of the following two conditions is satisfied.

(a)

$E(BL2) > c_1 \times E(BL1)$

(b)

$E(BL3) < c_2 \times E(BL1) .and. E(BL3) < c_3\times E(BL2)$

(ETH, c₁, c₂, c₃) are parameters to be optimized for each detector geometry.

To find out optimum value of clustering parameters, we generated two photons whose opening angle is some fixed value and study the efficiency to be clustered to two clusters. The energy of photon is generated randomly in betwen 1 GeV to 50 GeV and $\cos\theta$ range is from -0.7 to 0.7 so as to cover barrel Elemag calorimeter region. The azimuthal angle is from 0 to 360$^\circ$. The obtained figure is shown in Fig. 4. In this figure, the opening angle of two photon is 50mrad.

  

Figure 4: The efficiency to cluster into two cluster when two photons are generated. The opening angle between two photons is fixed at 50 mrad. The energy of two photons are same, but changes event by event between 1 to 50 GeV.

  

Figure 5: Same as Fig. 4, but with 100 mrad opening angle between photons.

  

Figure 6: The efficiency to cluster to one when one photon is generated. The energy of photon is same, but changes event by event between 1 to 50 GeV.

  

Figure: Same as Fig. 4 for the case of Endcap Elemeg Calorimeter. First photon is generated with the $\cos\theta$ range from 0.79 to 0.96. Second photon is generated with the opening angle of 50 mrad and same energy.

  

Figure 8: Same as Fig. 7, but with 100 mrad opening angle between photons.

  

Figure 9: The efficiency to cluster to one when one photon is generated. The energy and the angular range is same as Fig. 7.

Conclusions from parameter study

For 1 photon reconstruction in Barrel EM calorimeter(Fig. 6), $c_1 \leq 0.4$, $c_2 \geq 0.2$, $c_3\geq 0.3$ for high efficient clustering. For two photons with 100 mrad separation in Barrel EM calorimeter (Fig. 5), requirement to the clustering parameters for efficient clustering is, 0.3 < c₁ < 0.5, c₂ > 0.2, c₃ > 0.5.

Parameters of EM calorimeters are summarized in the Fig. 10.

  

Figure 10: parameters of EM calorimeter.

As seen in the figure, phi segmentation is about 25 mrad. Therefore, if opening angle between two photon is 50 mrad, EM hit cell is quite over lap and it is hard to separate them with high efficiency. It requires about 100 mrad separation to high efficient cluster separation.

As a conclusion, current default value of clustering is good for both barrel and end cap EMC calorimeter.