Antineutron reconstruction in electromagnetic calorimeters with mixed-representation learning

Technical Summary: Antineutron Reconstruction in Electromagnetic Calorimeters with Mixed-Representation Learning

Problem Statement
Reconstructing long-lived neutral hadrons (such as antineutrons, neutrons, and $K^0_L$ mesons) in GeV-scale accelerator experiments remains a significant bottleneck. These particles produce no ionization trajectories in tracking systems, forcing reliance on calorimeter subsystems. However, conventional electromagnetic calorimeters (ECALs) are optimized for electromagnetic showers (bremsstrahlung and pair production) rather than the complex hadronic interactions (nuclear scattering, spallation, and annihilation) characteristic of neutral hadrons. Consequently, antineutron interactions in ECALs yield sparse, fragmented, and non-local energy deposition signatures that standard clustering algorithms fail to reconstruct robustly. This limitation degrades invariant mass resolution, hinders background suppression, and restricts the physics reach of experiments studying hyperon decays, baryon spectroscopy, and exotic hadron searches. Furthermore, existing machine learning (ML) approaches for calorimeter reconstruction have largely focused on the detector's native operating regime or relied on simulation data that may not accurately reflect real-world discrepancies, particularly for neutral hadrons in the sub-GeV region.

Methodology: Mixed-Representation Calorimetric Network (MrCAL)
To address these challenges, the authors propose a physics-inspired mixed-representation learning approach, implemented via the Mixed-representation Calorimetric Network (MrCAL). The core insight is that antineutron responses in ECALs exhibit two distinct, complementary regularities:

1. Individual Event Level: Responses are sparse, stochastic, and spatially non-local, with energy deposits scattered across disconnected regions.
2. Population Level: When averaged over many events, a reproducible spatial prior emerges, characterized by a central concentration around the incident point and a radial, diffusion-like attenuation profile.

MrCAL integrates these patterns within a unified object-detection framework using two complementary branches:

• Visual Representation Branch: This branch maps calorimeter cell readouts onto a 2D image to capture the statistically stable, averaged spatial prior. It employs a physics-inspired diffusion operator (based on a 2D heat conduction equation) to encode the centrality-and-diffusion pattern, transforming sparse local activations into broad shower morphology features. The branch utilizes a RetinaNet-based architecture with a Feature Pyramid Network (FPN) to perform object detection. To handle the target being an incident point rather than a physical object extent, the method uses pseudo bounding boxes centered on labeled incident positions for supervision.
• Sequential Representation Branch: This branch captures event-by-event fluctuations by encoding active calorimeter cells as a token sequence. It utilizes a Transformer-based architecture to model long-range dependencies and non-local correlations among dispersed deposits, which is more information-efficient for sparse events. Each token represents a hit's energy and angular coordinates. The branch employs a "position-cloze" pretraining strategy, where the model predicts masked angular coordinates from energy prompts and surrounding context, allowing it to learn spatial patterns without relying solely on incident labels.
• Fusion Mechanism: The two branches operate in parallel, processing the same ECAL data through different representations. During inference, candidate detections from both branches are generated independently and then reconciled based on class consistency, angular agreement, and confidence scores. The final output is a unified set of predictions for particle identity, incident direction, and momentum magnitude.

Key Contributions and Results
The authors evaluated MrCAL using a large corpus of real collision data from the BESIII experiment, comprising over 5 million events across 36 decay channels (including $J/\psi$, $\psi(2S)$, and $e^+e^-$ annihilation data). The study utilized a momentum-balanced sample for training and testing, with specific channels held out for generalization tests.

• Directional Precision: MrCAL significantly improves the reconstruction of the antineutron momentum direction. Compared to a conventional clustering baseline, the mean angular bias (mAB) was reduced from $23.2^\circ$ to $11.8^\circ$ at full efficiency in single-particle settings. This represents a 96% improvement in directional precision.
• Momentum Magnitude: For the first time, the paper demonstrates the ability to directly measure momentum magnitude solely from ECAL readouts for antineutrons. At 1 GeV/c, the model achieves a momentum resolution of approximately 17% (specifically 17.6% for MrCAL), outperforming typical resolutions of dedicated hadronic calorimeters in the sub-GeV regime.
• Robustness and Generalization: The model maintains stable performance across diverse kinematic regions and complex multi-particle environments (e.g., antineutrons accompanied by photons). In generalization tests involving 13 channels completely excluded from training, the directional precision improvements persisted, with average gains of 59.8% in single-particle settings and 31.0% in multi-particle settings.
• Physics Impact: The reconstructed antineutron four-momenta were successfully used to reconstruct short-lived mother particles (e.g., $\Lambda$, $\Sigma^\pm$, $J/\psi$), yielding clear invariant mass peaks with unbiased central positions. The average invariant mass resolution improved to 3.3% in single-particle settings.

Significance and Claims
The paper claims that MrCAL unlocks a novel measurement capability for legacy ECAL systems, effectively expanding their scientific scope without requiring hardware upgrades. By reframing neutral hadron reconstruction as an inverse problem solvable through mixed-representation learning, the approach mitigates a structural limitation that has persisted in many particle physics experiments.

The authors emphasize that their method is purely algorithmic and can be deployed on existing data. This is particularly significant for experiments like BESIII, where improved antineutron reconstruction directly benefits analyses of CP violation, quantum number violation, and baryon spectroscopy. The work suggests a broader paradigm shift where detector design and ML representational capacity are co-optimized, moving beyond the rigid separation of electromagnetic and hadronic calorimetry to leverage high-granularity raw data for ML-driven inference. The findings indicate that the current performance limits are likely set by detector design and intrinsic hadronic shower fluctuations rather than algorithmic deficiencies.