# Performance Study of a New Cluster Splitting Algorithm for the Reconstruction of PANDA EMC Data

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## Abstract

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## 1. Introduction

## 2. Cluster Splitting Algorithm

## 3. Lateral Energy Distribution of Electromagnetic Shower Considering the Detector Granularity

## 4. Performance Results

## 5. Summary

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- PANDA Collaboration. Technical Design Report for PANDA Electromagnetic Calorimeter (EMC). arXiv
**2008**, arXiv:0810.1216. [Google Scholar] - Panda Collaboration. Update to the Technical Design Report for the PANDA Electromagnetic Calorimeter. 2020. Available online: https://panda.gsi.de/system/files/user_uploads/heinsius%40ep1.rub.de/RE-TDR-2020-007.pdf (accessed on 30 July 2022).
- Eissner, T. The new PWO Crystal Generation and Concepts for the Performance Optimisation of the PANDA EMC. Available online: http://geb.uni-giessen.de/geb/volltexte/2013/10382 (accessed on 30 July 2022).

**Figure 1.**Side view of $\overline{\mathrm{P}}$ANDA with the target spectrometer (TS) on the left side and the forward spectrometer (FS), starting with the dipole magnet center, on the right side. The antiproton beam enters from the left.

**Figure 2.**The angle between the two final-state photons with the increase in the energy of ${\pi}^{0}$.

**Figure 3.**Demonstration of calculating the energy deposition fraction from seeds (red) for a target crystal (grey). ${f}_{1},{f}_{2},{f}_{3},$ and ${f}_{4}$ are energy fractions; ${\left({E}_{\mathrm{seed}}\right)}_{1}$, ${\left({E}_{\mathrm{seed}}\right)}_{2}$, ${\left({E}_{\mathrm{seed}}\right)}_{3}$, and ${\left({E}_{\mathrm{seed}}\right)}_{4}$ are different seed crystal energies; and ${r}_{1},{r}_{2},{r}_{3},$ and ${r}_{4}$ are the distances from the center of showers to center of target crystals.

**Figure 4.**The ${E}_{\mathrm{target}}/{E}_{\mathrm{seed}}$ varies with the r. The r is the distance from the shower center to the target crystal. Each point in the scatter plot represents a target crystal in the showers with the energy ${E}_{\mathrm{target}}$. The black dashed line is the empirical exponential function; the red line represents the fitting analytic function.

**Figure 5.**This figure shows a case in which the center of the shower is inconsistent with the center of the seed crystal. The green point is the center of the target crystal, and the blue point and yellow point represent the geometric center of the seed crystal and the center of the shower, respectively.

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## Share and Cite

**MDPI and ACS Style**

Zhang, Z.; Zhao, G.; Sun, S.; Pu, Q.; Liu, C.; Yu, C.; Liu, D.; Qi, H.; Huang, G.; Stockmanns, T.;
et al. Performance Study of a New Cluster Splitting Algorithm for the Reconstruction of PANDA EMC Data. *Instruments* **2022**, *6*, 34.
https://doi.org/10.3390/instruments6030034

**AMA Style**

Zhang Z, Zhao G, Sun S, Pu Q, Liu C, Yu C, Liu D, Qi H, Huang G, Stockmanns T,
et al. Performance Study of a New Cluster Splitting Algorithm for the Reconstruction of PANDA EMC Data. *Instruments*. 2022; 6(3):34.
https://doi.org/10.3390/instruments6030034

**Chicago/Turabian Style**

Zhang, Ziyu, Guang Zhao, Shengsen Sun, Qing Pu, Chunxiu Liu, Chunxu Yu, Dong Liu, Hang Qi, Guangshun Huang, Tobias Stockmanns,
and et al. 2022. "Performance Study of a New Cluster Splitting Algorithm for the Reconstruction of PANDA EMC Data" *Instruments* 6, no. 3: 34.
https://doi.org/10.3390/instruments6030034