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A graph neural network for deep learning-based full event interpretation at FCC-ee

This paper presents a deep learning-based graph neural network prototype for the FCC-ee IDEA detector that successfully reconstructs hierarchical $b$ -hadron decay trees from charged particle data, achieving over 90% accuracy in identifying the correct particle sets across various decay chains.

Original authors: Elena Graverini, Samuel Morand, Rafael Silva Coutinho, Felipe Luan Souza de Almeida

Published 2026-10-06

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CC BY 4.0

Original authors: Elena Graverini, Samuel Morand, Rafael Silva Coutinho, Felipe Luan Souza de Almeida

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the subatomic world, particles do not exist in isolation; they are born from collisions and immediately begin to decay, breaking apart into a cascade of new particles that themselves may decay again. This process creates a complex family tree, or decay chain, where a single heavy particle can spawn dozens of descendants before the chain finally ends in stable, detectable fragments. For physicists studying the fundamental forces of nature, understanding these trees is essential. By reconstructing exactly which particles came from which parent, they can test the laws of physics with extreme precision. However, in a high-energy collision, thousands of particles fly out in all directions at once, creating a chaotic mess where it is incredibly difficult to tell which fragments belong to which original family. The challenge is not just to see the particles, but to sort them into their correct lineages without any prior knowledge of what those lineages should look like.

To address this sorting problem, researchers have developed a new approach using a type of artificial intelligence known as a graph neural network. This method treats a collision event not as a list of data points, but as a map where every detected particle is a point, and the connections between them are the relationships the network must learn to identify. The goal is to build a system that can look at the final spray of particles and automatically group them back into their original decay families, effectively reversing the explosion to reveal the hidden history of the event. This capability is particularly crucial for the Future Circular Collider, a proposed machine that will smash electrons and positrons together to produce billions of heavy particles. Because this future machine will generate data at a scale far beyond current capabilities, scientists need tools that can interpret entire events instantly and accurately, rather than just focusing on specific, pre-defined outcomes.

A team of physicists has now created and tested a prototype of such a system, designed specifically for the conditions expected at the Future Circular Collider. They focused on events where an electron and a positron collide to produce a Z boson, which then decays into a pair of heavy bottom quarks. These quarks immediately transform into heavy particles called b-hadrons, which then decay into a shower of lighter charged particles. The researchers simulated these collisions using a detailed model of a proposed detector called IDEA, which is designed to capture nearly every particle flying out from the collision point. In their simulation, they fed the network information about the paths and speeds of every reconstructed charged particle in an event, asking the system to figure out which particles belonged to the same decay chain and how they were related to one another.

The network was trained to look for patterns in the way particles move and interact. Instead of being told what a specific decay looks like, the system learned to recognize the geometric and kinematic signatures that link particles together. It treated the event as a web, where every particle is connected to every other particle, and it had to decide which connections were real family ties and which were just random coincidences. The researchers found that the system was remarkably good at this task. In their tests, the network successfully grouped the correct set of particles together about 89 percent of the time for general collision events. This means that even without knowing the specific details of the decay in advance, the AI could reliably identify the right family members from the crowd.

When the researchers tested the system on specific, well-known types of decays, the performance was even higher, with success rates reaching up to 97 percent. The system proved especially robust at identifying the correct group of particles, even when the internal structure of the family tree was complex. However, the study also revealed a specific limitation. While the network was excellent at gathering the right particles into a single group, it sometimes struggled to determine the exact order in which they were born. In about 39 percent of the general test cases, the system got the entire family tree structure perfectly right, including the precise hierarchy of who was the parent and who was the child. In the remaining successful cases, it got the right group of particles but made mistakes about the internal relationships, such as confusing a grandchild with a child.

This distinction is important because it shows that the primary difficulty for the AI is not finding the right particles, but rather reconstructing the exact sequence of their creation. The researchers observed that as the decay chains became longer and more complex, the ability to get the perfect internal order dropped, yet the ability to keep the correct particles together remained high. This suggests that the system has mastered the art of clustering, which is the most critical step for many physics analyses, even if the fine details of the family tree are still being refined. The study also looked at how fast the system could run, finding that it could process events very quickly on modern computer processors, making it a viable candidate for the high-speed data analysis required by future colliders.

The work represents a significant step forward in how physicists plan to handle the massive amounts of data expected from the next generation of particle accelerators. By demonstrating that a graph-based approach can reconstruct complex decay trees from scratch, the team has shown that it is possible to move beyond rigid, pre-programmed rules for identifying particles. Instead, the system learns the underlying logic of particle decay directly from the data. While the current prototype focuses only on charged particles and does not yet include neutral ones, the results provide a strong foundation for future developments. The researchers envision a future where such systems can interpret entire collision events in real-time, filtering out the noise and preserving only the most interesting decay chains for deeper study. This capability would allow scientists to explore rare and subtle phenomena that might otherwise be lost in the sheer volume of data, opening new windows into the fundamental structure of the universe.

Technical Summary: Graph Neural Network for Deep Learning-Based Full Event Interpretation at FCC-ee

Problem Statement
Future Circular Collider (FCC-ee) operations, particularly at the $Z$ boson resonance ( $\sqrt{s} = 91$ GeV), will generate unprecedented event samples ( $\sim 6 \times 10^{12}$ $Z$ bosons). A critical challenge in analyzing these events is the "Full Event Interpretation" (FEI) of heavy-flavor decays. Specifically, reconstructing the hierarchical decay trees of $b$ -hadrons from a sea of reconstructed charged particles is difficult. Traditional approaches, such as the Belle II FEI algorithm, rely on hierarchies of boosted decision trees trained on specific, exclusive decay channels, limiting their applicability to rare or unmodeled decays. While Deep Learning-based FEI (DFEI) has been explored at LHCb for inclusive $b\bar{b}$ samples, its application to the cleaner, high-precision environment of the FCC-ee, utilizing the Innovative Detector for Electron positron Accelerators (IDEA) concept, requires validation. The core problem addressed is the simultaneous identification of particles belonging to specific $b$ -hadron decay chains and the reconstruction of their internal hierarchical relationships without predefined decay hypotheses.

Methodology
The authors propose a Graph Neural Network (GNN) framework where each event is represented as a fully connected undirected graph.

Graph Representation: Reconstructed charged particles serve as nodes, containing kinematic features (momentum components, charge, $p_T$ , $\eta$ ) and track parameters (helix parameters $d_0, z_0, \phi_0, \tan\lambda, \omega$ and their significances). Edges connect every pair of particles and encode pairwise observables, including opening angles, distances of closest approach (DOCA), and momentum sums.
Labels (Ground Truth): The target labels are derived from "topologized" ground truth decay trees. Intermediate particles are pruned if they do not support at least two downstream reconstructed branches. The hierarchical relationship between any two particles is encoded using Least Common Ancestor Generation (LCAG) labels. In this scheme, reconstructed leaves are generation 0, and ancestors are assigned increasing generations. If no common ancestor exists within the decay tree, the label is 0.
Model Architecture: The network utilizes a sequence of graph-network blocks following the framework of Ref. [12]. A distinctive feature is the inclusion of learned gates during message passing (inspired by Ref. [27]). These gates modulate the information flow between nodes and edges, suppressing less informative relations in the fully connected graph. The architecture includes node and edge update functions ( $\phi_v, \phi_e$ ) and gating functions ( $\psi_v, \psi_e$ ) implemented as MLPs and linear layers with sigmoid activation, respectively.
Training Objective: The primary task is a multiclass classification of LCAG labels (classes 0–3). Due to class imbalance (90% class 0), the model employs class weights. Two loss functions are evaluated: weighted cross-entropy and focal loss. Additionally, auxiliary binary cross-entropy losses ( $L_{node}$ and $L_{edge}$ ) are applied to constrain the learned gates, ensuring they align with whether particles originate from a $b$ -hadron decay or belong to the same decay tree. The total loss is a weighted sum of the LCAG loss and the auxiliary gate losses.
Inference: The model predicts LCAG probabilities for all particle pairs. A connectivity threshold ( $t_{conn}$ ) determines if two particles belong to the same cluster (decay chain candidate). Clusters are then analyzed to reconstruct the internal hierarchy based on non-zero LCAG predictions.

Key Contributions

First DFEI Prototype for FCC-ee: This work presents the first application of a signal-agnostic, deep learning-based full event interpretation framework specifically designed for the FCC-ee environment using the IDEA detector concept.
Signal-Agnostic Approach: Unlike previous methods tied to specific decay modes, this model is trained on inclusive $e^+e^- \to Z \to b\bar{b}$ samples, enabling the reconstruction of rare or unmodeled decays.
Gated Graph Architecture: The integration of learned gates within the graph network blocks allows the model to dynamically regulate information propagation, addressing the noise inherent in fully connected graphs of high-multiplicity events.
Comprehensive Evaluation: The study evaluates performance across inclusive samples and a diverse set of exclusive benchmark channels, including rare flavor-changing neutral currents and high-yield hadronic decays.

Results

Inclusive Performance: On an inclusive test sample of 10,000 $e^+e^- \to Z \to b\bar{b}$ $e^{+} e^{-} \to Z \to b \overset{ˉ}{b}$ events, the model achieved a clustering efficiency of 89.4%. This metric (sum of "Perfect" and "Wrong Hierarchy" categories) indicates the model successfully identifies the correct set of particles for a decay chain.
- Perfect Reconstruction: 38.7% of decay trees were reconstructed with both the correct particle content and the correct internal hierarchy.
- Wrong Hierarchy: 50.6% of trees had the correct particles but incorrect internal hierarchy.
- Contamination/Partial: Contaminated total and partial reconstructions accounted for ~5% and ~4%, respectively.
Exclusive Performance: Performance improved on exclusive benchmark channels (topological depth 1–2), with clustering efficiencies ranging from 93% to 97% and perfect reconstruction fractions exceeding 66%. Simple two-body decays (e.g., $B^0 \to K^+\pi^-$ ) reached 97% perfect reconstruction.
Complexity Dependence: As the number of reconstructed particles and the topological depth of the decay tree increased, the "Perfect" reconstruction fraction decreased, while the "Wrong Hierarchy" fraction increased. However, the clustering efficiency remained stable (85–90%), suggesting the model reliably identifies particle membership even when the exact hierarchy is ambiguous.
Computational Performance: Inference latency on GPUs (NVIDIA A100, Quadro RTX 4000) remained approximately constant at 5–7 ms per event for the studied track multiplicities, significantly outperforming single-threaded CPU configurations.

Significance and Claims
The paper positions this work as a proof of concept for graph-based event interpretation at FCC-ee. The authors claim that the results demonstrate the feasibility of reconstructing heavy-hadron decay trees from charged particles in a signal-agnostic manner. The high clustering efficiency indicates that the model can reliably isolate the correct set of particles associated with a decay chain, which is a prerequisite for precision flavor physics measurements.

The authors explicitly state that the primary limitation of the current prototype is the inference of the exact internal hierarchy rather than particle identification. They note that the study is restricted to charged particles and does not yet include particle identification (PID) or neutral particles. Future work is identified as necessary to extend the framework to neutral particles (potentially using heterogeneous GNNs) and to reconstruct richer decay tree information, such as particle identities, to fully realize a comprehensive event interpretation framework for FCC-ee.

Technical Summary: Graph Neural Network for Deep Learning-Based Full Event Interpretation at FCC-ee

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