Using Graph Neural Networks for hadronic clustering and to reduce beam background in the Belle~II electromagnetic calorimeter

This paper proposes a novel Graph Neural Network approach to mitigate the challenges of increased beam background and irregular hadronic interactions in the Belle~II electromagnetic calorimeter by representing crystal energy depositions as sparse graphs to effectively identify and remove unwanted noise before clustering.

The Gist

Imagine the Belle II experiment as a giant, ultra-sensitive camera trying to take a perfect photo of a fireworks display. This camera is located in a particle accelerator in Japan, where tiny particles smash into each other at incredible speeds.

The "camera" in question is the Electromagnetic Calorimeter (ECL). It's made of thousands of crystal blocks (like giant ice cubes) that light up when particles hit them. Scientists use these flashes of light to figure out what kind of particles were created in the crash.

The Problem: A Messy Room

Recently, the accelerator has been running at record-breaking speeds. While this is great for science, it's a nightmare for the camera.

1. Too Much Noise: The high speed creates a lot of "static" or background noise (like people shouting in a crowded room). This noise hits the crystals, creating false flashes of light that look like real fireworks.
2. Messy Fireworks: Some particles (called hadrons) don't just make a clean, round flash like a photon (light particle) does. They scatter, break apart, and hit crystals far away from the main explosion. It's like throwing a handful of confetti that lands in a messy, disconnected pile rather than a neat circle.

The Old Way of Sorting:
Currently, the computer tries to group these flashes into "clusters" (like grouping confetti into a single pile). It uses a simple rule: "If two flashes are close together and bright enough, they belong to the same pile."

But because there is so much noise and the messy confetti is so irregular, the computer gets confused. It creates:

• Fake Piles: Grouping noise together as if it were a real particle.
• Split Piles: Breaking one real particle's mess into two or three separate piles.
• Slow Processing: It takes too long to sort through all this junk.

The Solution: A Smart Detective (The Graph Neural Network)

The authors of this paper propose a new tool: a Graph Neural Network (GNN). Think of this not as a simple rule-book, but as a super-smart detective who understands relationships.

Instead of just looking at individual flashes, the GNN looks at the whole picture as a connected web (a graph).

• The Nodes: Each crystal that lit up is a "node" (a person in a crowd).
• The Edges: The connections between them are the "relationships" (who is standing next to whom).

How the Detective Works:

1. Seeing the Sparsity: The detector is mostly empty space with a few flashes. The GNN is great at ignoring the empty space and focusing only on the active crystals.
2. Understanding the Shape: Because the crystals in the detector are arranged in a weird, tilted way, the GNN learns the unique geometry of the room. It knows, "Ah, this crystal is far away from that one, so they probably aren't part of the same event," even if they are both lit up.
3. The Filter: Before the computer tries to group the flashes into clusters, the GNN acts as a bouncer. It looks at every "flash" (Local Maximum) and asks: "Is this a real signal, or is it just background noise or a messy split-off?"

The Training: Teaching the Detective

To teach this AI, the scientists used a massive simulation of the detector. They labeled the data like a teacher grading a test:

• Signal: The good, real fireworks.
• Beam Background: The static noise from the accelerator.
• Split-offs: The messy confetti that broke away.
• Duplicates: Mistakes where the computer counted the same thing twice.

They fed this data to the GNN, letting it learn the subtle differences between a real particle and a fake one.

The Results: Cleaning Up the Mess

When they tested the new system:

• Noise Removal: It successfully identified and removed about 90% to 95% of the background noise (the "shouting crowd") without accidentally throwing away the real fireworks.
• Messy Confetti: It was a bit harder to fix the "split-off" mess (the scattered confetti), but it still managed to clean up about 40% of those errors in the best areas.
• Speed: By removing the junk before the clustering happens, the whole process becomes faster and the final data is much cleaner.

The Big Picture

In simple terms, this paper says: "The old way of sorting particle data is getting overwhelmed by noise and messy shapes. By using a smart AI that looks at the connections between crystals, we can filter out the garbage before we try to make sense of the data. This means cleaner photos of the universe and faster science."

This is a crucial step forward for the Belle II experiment, ensuring that as the accelerator gets even faster in the future, the scientists can still see the beautiful physics happening amidst the chaos.

Technical Summary

1. Problem Statement

The Belle II experiment at the SuperKEKB accelerator operates at record-breaking instantaneous luminosities ($\approx 5 \times 10^{34} \text{ cm}^{-2}\text{s}^{-1}$), which has introduced significant challenges for the Electromagnetic Calorimeter (ECL). The current clustering algorithm, which relies on Connected Regions (CR) and Local Maxima (LM), faces two primary issues:

• Increased Beam Background: High luminosity leads to increased rates of beam-induced background processes (e.g., Touschek effect, radiative Bhabha scattering, synchrotron radiation). This results in a higher number of crystals with energy depositions, creating spurious LMs that degrade photon energy resolution and increase the rate of fake photon clusters.
• Hadronic Interaction Complexity: Unlike electromagnetic showers, hadronic interactions produce irregular, sometimes disconnected energy depositions. This leads to "split-offs" (secondary particles like neutrons traveling significant distances before interacting) and multiple LMs within a single shower. The current algorithm often misinterprets these as separate photon clusters, reducing position resolution for neutral hadrons or causing misidentification.

These issues lead to increased computational runtimes, larger file sizes, and difficulties in analyses that rely on precise energy conservation (collision energy matching).

2. Methodology

The authors propose a Graph Neural Network (GNN) based classification algorithm designed to identify and filter unwanted LMs before the standard clustering process begins.

2.1 Data Labeling and Training Targets

To train the model, the authors utilized the Belle II Analysis Software Framework (basf2) and Geant4 simulations to categorize LMs into specific classes:

• Signal: LMs associated with primary particles or valid root particles (e.g., $\pi^0$, $K^0_S$).
• Beam Background: LMs with $<20$ MeV deposited energy from simulated particles, originating from beam-related background processes.
• Duplicate LMs: LMs not associated with any simulated particle (artifacts of the simulation or reconstruction).
• Split-offs: LMs associated with secondary particles created during hadronic showers that travel significant distances before interacting again.

Novel Simulation Handling: The paper introduces new conditions to store secondary particles in simulation that were previously attributed to their parent. This allows for the explicit identification of "split-off" particles based on kinetic energy thresholds and vertex distances ($>40$ cm) in the outer detector regions.

2.2 Graph Construction

• Nodes: Represent individual crystals containing energy measurements.
• Features: Measured energy, time, detailed pulse-shape template fit information, and crystal mass (to account for geometric variations).
• Topology: For each target LM, a graph is constructed using neighbors up to the 5th order (a $9\times9$ square in the barrel). Due to the small size of these graphs, they are treated as fully connected with unweighted edges.

2.3 Model Architecture

The network architecture is based on existing works but includes specific optimizations:

• Global Exchange: Appends graph-wide averages to node features.
• Embedding: Uses BatchNormalization and linear layers to create node embeddings.
• Message Passing: A stack of blocks using a modified GravNet layer. Crucially, the K-nearest-neighbor calculation is skipped; instead, all nodes are connected, and distances are used as weights in the message passing. This significantly improves training speed and stability.
• Output: Feed-forward layers provide a classification probability (Signal vs. Background).
• Training Strategy: Trained on 20,000 $\Upsilon(4S) \to B\bar{B}$ events and 10,000 $e^+e^- \to \phi\gamma$ events. Stochastic Weighted Averaging (SWA) is applied after 100 epochs for stability. Mean Squared Error (MSE) is used as the loss function.

2.4 Threshold Determination

The classifier is applied only to LMs with measured energies between 20 MeV and 100 MeV.

• Working Point: Set to maintain a 95% signal efficiency (5% signal rejection).
• Binning: Thresholds are calculated separately for each detector region (Forward, Barrel, Backward) and in bins of measured energy to avoid bias from low-energy LMs.
• Smoothing: Cubic spline interpolation is used between bin centers.

3. Key Results

The classifier was evaluated on independent simulated data with beam background overlays:

• Beam Background Removal: The GNN achieves a ~90–95% rejection rate for beam-background-induced LMs while maintaining 95% signal efficiency. This is the most successful category due to the distinct nature of background signatures.
• Split-offs and Duplicate LMs: Rejection rates are lower due to the physical similarity between these backgrounds and true signal showers.
  • In the Barrel region (specifically $>50$ MeV), the rejection rate for these challenging classes reaches ~40%. This improvement is linked to the precision of pulse-shape fits at higher energies.
  • In the Forward and Backward endcaps, efficiency is lower (30–50%) due to higher background levels and geometric complexities.
• Overall Performance: At low LM energies, the classifier achieves an average rejection efficiency of ~75% across all background types, dropping to ~30–50% in specific regions where beam background dominates or pulse-shape information is less reliable.

4. Key Contributions

1. GNN Application for Pre-Clustering: Proposes a novel GNN approach to filter LMs prior to the standard clustering algorithm, addressing the sparsity and asymmetry of the Belle II ECL layout more effectively than traditional methods.
2. Enhanced Simulation Labeling: Introduces a rigorous definition and simulation protocol for "split-off" particles, enabling the creation of a high-quality training dataset that distinguishes between signal, beam background, and complex hadronic split-offs.
3. Optimized Architecture: Demonstrates that removing K-nearest-neighbor calculations in favor of fully connected graphs with distance-weighted message passing improves training convergence and stability for small detector graphs.
4. Region-Specific Tuning: Develops a dynamic thresholding strategy that accounts for the varying background densities and detector geometries across the Forward, Barrel, and Backward regions.

5. Significance

This work addresses a critical bottleneck in the Belle II experiment's ability to handle high-luminosity data. By effectively removing spurious LMs caused by beam background and hadronic split-offs:

• Physics Performance: Photon energy resolution and neutral hadron position resolution are improved, reducing fake cluster rates.
• Computational Efficiency: Reducing the number of false LMs decreases the runtime of downstream clustering algorithms and reduces data storage requirements.
• Future Impact: The methodology establishes a framework for using GNNs to clean detector data before reconstruction, which is expected to benefit future developments in cluster energy prediction and particle identification in high-luminosity environments.