Photon reconstruction using the Hough transform in imaging calorimeters

TL;DR

The paper introduces an energy-core based photon reconstruction method for imaging calorimeters by extending the Hough transform to detect the energy-core axis of electromagnetic showers. It combines clustering, a generalized Hough transform, and a two-stage energy-splitting algorithm to resolve overlapping showers, validated on a CEPC crystal ECAL simulation. The results show near 100% single-photon reconstruction efficiency for energies above 2 GeV and near 100% two-photon separation when showers are spaced at the calorimeter granularity limit. This method reduces reliance on detailed shower boundaries, improves photon measurement in high-multiplicity events, and is readily generalizable to other calorimeter technologies and particle-flow applications.

Abstract

Photon reconstruction in calorimeters represents a crucial challenge in particle physics experiments, especially in high-density environments where shower overlapping probabilities become significant. We present an energy-core-based photon reconstruction method. It is achieved through extending the application of the Hough transform to exploit the energy-core structure of photon showers. The method, validated through simulations of the CEPC crystal electromagnetic calorimeter, demonstrates outstanding performance. It achieves a reconstruction efficiency of nearly 100% for photons with energies exceeding 2 GeV and a separation efficiency approaching 100% for two 5 GeV photons, when the distance between them reaches the granularity limit of the calorimeter. This energy-core-based photon reconstruction method, integrated with an energy splitting technique, enhances the performance of photon measurement and provides a promising tool for imaging calorimeters, particularly those requiring high precision in photon detection in complex event topologies with high multiplicity.

Figures (10)

• Figure 1: Basic structure of the crystal ECAL. A single crystal bar, with typical dimensions of $1.5\times1.5\times\sim40 \text{cm}^3$, is read out at both ends. Crystals in adjacent layers are oriented perpendicularly to each other. Multiple layers are stacked to form a test module.
• Figure 2: Two-dimensional energy deposition distribution of a 5 GeV photon shower, with the x-axis and y-axis representing longitudinal and lateral directions respectively. A compact energy-core is observed along the direction of shower development.
• Figure 3: Global view of the barrel ECAL (left) and schematic of two adjacent trapezoidal modules (right).
• Figure 4: Example of the energy deposition distribution of crystals in one layer, for a photon of 5 GeV, where each bin corresponds to a crystal. Crystals satisfying the local maximum condition are highlighted. The vertical dotted line indicates the true position of the shower
• Figure 5: Spatial distribution of crystals for a 5 GeV photon, with local maxima highlighted. The color scale represents the energy deposition, with the energy threshold (0.5 MIP) of local maxima indicated on the color bar. Local maxima are marked with dot patterns.