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"Transforming" LHCb: self-supervised maps of heavy-flavour decays

This paper proposes and validates a self-supervised transformer architecture that learns heavy-flavour decay maps from LHCb data without explicit labels, demonstrating improved tagging performance and the ability to detect decays with invisible particles by inferring masked particle information and identifying anomalies in reconstructed jets.

Original authors: Marko Stamenkovic, Greg Landsberg

Published 2026-09-10

📖 4 min read🧠 Deep dive

CC BY 4.0

Original authors: Marko Stamenkovic, Greg Landsberg

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

The universe is built from a handful of fundamental particles, but the most interesting stories often happen when these particles decay, transforming into lighter, more stable forms. In the high-energy collisions at the Large Hadron Collider, heavy versions of these particles, known as beauty and charm hadrons, are created in vast numbers. When they break apart, they leave behind a trail of other particles that detectors can see. Physicists study these trails to find cracks in our current understanding of nature, looking for signs of invisible particles or strange behaviors that the standard model of physics cannot explain. However, finding these subtle signals is difficult because the detectors only see the visible pieces of the puzzle. If a heavy particle decays into something that leaves no trace, or if the decay is messy and incomplete, the standard tools for identifying what happened often fail. The challenge is to learn how to read the full story of a decay just by looking at the fragments that remain, even when some of the story is missing.

Researchers at Brown University have developed a new way to teach computers how to understand these heavy-particle decays without needing a textbook of answers. Instead of showing the computer millions of examples with the correct labels, they let the machine learn the rules of the game by trying to fill in the blanks. They took a massive dataset of simulated collisions from the LHCb experiment and presented the computer with jets—sprays of particles created in the collision—where they deliberately removed some of the tracks or hid their identities. The computer's task was to guess what was missing. By repeatedly trying to reconstruct the full picture from incomplete information, the system learned a deep, internal map of how heavy particles usually break apart. This map captures the complex relationships between the particles, such as how they move, where they come from, and what they are, without ever being told the specific name of the parent particle.

Once the computer had learned this map, the researchers tested whether it actually understood the physics. They found that the system could distinguish between different types of heavy particles and even tell the difference between matter and antimatter versions of the same particle, performing just as well as traditional methods that rely on fully labeled data. More importantly, they tested if the system could spot when a real decay was incomplete. When they took a reconstructed decay from a real collision and removed a known piece of it, the computer's "missingness score" went up significantly, indicating that the jet looked less complete than it should. This reaction was much stronger than when they removed random, unrelated particles from the same jet. This suggests the system has learned the specific, coherent structure of a heavy-particle decay and can sense when that structure is broken.

The team then took this trained system and applied it to real data from proton-proton collisions recorded in 2017. Without any further training on this specific data, the system successfully identified the same patterns in real-world collisions. It could separate different types of heavy-flavor decays and responded to the removal of specific particles in the real data just as it did in the simulations. The researchers also used the system to explore the data for unusual patterns. They found a small group of jets that looked very different from the rest: they were packed with charged particles but had almost no neutral ones. While the researchers could not immediately say what caused this, the system successfully organized these strange events together, showing that the method can group similar anomalies for further investigation.

This work demonstrates that a computer can learn the language of particle decay directly from the data itself, without needing a human to write the dictionary first. By learning to complete the picture of a decay, the system gains a powerful ability to recognize when something is wrong or missing. This approach offers a new way to search for physics beyond our current understanding, particularly for rare or incomplete decays that might otherwise be hidden in the noise. The researchers have shown that by teaching machines to understand the structure of these events, we can open new windows into the invisible parts of the universe, potentially revealing new particles or forces that have so far remained out of reach.

Technical Summary: "Transforming" LHCb: self-supervised maps of heavy-flavour decays

Problem Statement
Heavy-flavour decays of beauty and charm hadrons serve as sensitive probes for physics beyond the Standard Model (BSM), particularly in scenarios involving invisible particles or incomplete final states (e.g., B-mesogenesis). While the LHCb experiment at CERN possesses the precise tracking, vertexing, and particle identification (PID) capabilities required to map these decay environments, current flavour tagging methods in LHCb rely heavily on secondary vertices and utilize the DeepSets architecture. These methods often underutilize the full fragmentation history, underlying event information, and pileup. Furthermore, existing taggers are not optimized for "incomplete" decays where parts of the final state leave no detector signature. The authors propose leveraging recent advances in jet flavour tagging from ATLAS and CMS—specifically the use of permutation-invariant particle clouds and transformer architectures—to improve LHCb's tagging performance and extend its reach to decays with invisible particles.

Methodology
The paper introduces a self-supervised learning framework that learns a "map" of heavy-flavour hadronization and decay environments directly from data, without relying on flavour or exclusive-decay labels.

Architecture: The core model is a particle set transformer. It ingests an unordered set of reconstructed jet constituents (up to 64 per jet), including kinematics, displacement information, and probabilistic PID responses from RICH and calorimeter systems. The encoder consists of five transformer blocks with an embedding dimension of 96 and eight attention heads.
Self-Supervised Task: The model is trained to perform two simultaneous tasks:
1. Masked PID Prediction: Predicting the PID class and response bins for surviving particles whose PID inputs are hidden.
2. Particle Set Completion: Predicting the properties (multiplicity, kinematics, charge, identity, and topology) of constituents that have been artificially removed from the jet view.
Data Augmentation: During training, zero to four reconstructed constituents are removed from a jet based on specific rules (random charged/neutral, opposite-sign pairs, angularly local groups, displaced vertices, or cascades). The model must infer the missing content based solely on the surviving particles and the global jet context.
Missingness Score ( $S_{miss}$ ): A key output is a score derived from the model's probability that a jet is incomplete. This score is calculated as the log-odds ratio of the model predicting an incomplete jet versus the baseline probability of artificial removal in the training set.
Training Data: The study utilizes two datasets:
1. Simulated LHCb Open Data: Dijet events ( $b\bar{b}$ , $c\bar{c}$ , light partons, $Z \to b\bar{b}$ ) generated with Pythia 8 and EvtGen, reconstructed with Geant4. This allows for controlled "intervention" tests where specific reconstructed resonances are removed.
2. 2017 LHCb Open Data (Collision Data): Inclusive proton-proton collision data used to train a separate model without any flavour labels, validating the method's applicability to real detector conditions.

Key Contributions

Self-Supervised Map Construction: The authors demonstrate that a transformer can learn a continuous representation of heavy-flavour decay environments by inferring masked PID information and completing jets with missing constituents, effectively creating a "hadronization and decay map."
Label Efficiency: The study shows that this self-supervised representation captures physically meaningful flavour and quark charge sign information. When used as a frozen feature extractor for affine probes (linear classifiers), it recovers 97–100% of the performance of a fully supervised transformer trained with all labels, using only a small fraction of labelled data.
Anomaly Detection via Intervention: The paper introduces a method to detect anomalies by systematically removing reconstructed decay candidates (e.g., $D^0$ , $B^+$ ) from jets and observing the increase in the missingness score. This validates that the model has learned the correlated structure of heavy-flavour decays.
Transfer to Collision Data: The method is validated on real 2017 LHCb collision data. A model trained independently on this data reproduces the expected "missingness" response when constituents of reconstructed charm and beauty decays are removed, confirming the learned map's relevance to physical events.

Results

Simulation Performance:
- The model distinguishes between complete and artificially incomplete jets with an Area Under the Curve (AUC) of 0.72 (inclusive), rising to 0.87 for jets with four removed constituents.
- In flavour tagging tasks (e.g., $b$ vs. $c$ , $b$ vs. light), the self-supervised probe significantly outperforms a transformer with random weights. For instance, in $b$ vs. $c$ classification, it achieves an AUC of 0.83 with only 0.1% of labelled training data, compared to 0.67 for random features.
- The tagging power ( $P_{tag}$ ) for inclusive $b$ -jets is calculated at 10.6%, and for $c$ -jets at 31.1%.
- Removing reconstructed $D^0 \to K\pi$ candidates from $b$ -jets in simulation results in a mean score shift of 4.05, significantly higher than the shift of 1.33 observed when removing matched random tracks from the same jet.
Collision Data Performance:
- A model trained on 2017 collision data (without flavour labels) responds systematically to the removal of constituents from eight reconstructed charm and beauty modes. For high-statistics charm modes, the signal response exceeds that of adjacent mass sidebands.
- Simulation-trained affine probes, when applied to 2017 collision data without retraining, successfully separate $B^+$ and $B^0$ flavour categories and prompt $D^0/D^+$ decays, demonstrating transferability.
- Exploratory analysis of high-missingness jets in collision data reveals distinct clusters based on similarity (e.g., a group of charged-rich, neutral-poor jets), suggesting the method can organize anomalous events for further inspection.

Significance and Claims
The paper claims to provide a proof of principle that mapping heavy-flavour decay environments through jets using self-supervised learning can transform flavour tagging in LHCb. The authors emphasize that:

The approach does not rely on exclusive decay labels or specific BSM hypotheses during the representation learning phase.
It successfully bridges the gap between simulated learning and real collision data, validating that the learned notion of "completeness" corresponds to physical decay structures.
The method offers a pathway to extend discovery reach to "incomplete" or unusual decays (including those with invisible particles) by identifying jets that deviate from the learned completion map.
The technique is complementary to existing taggers and could be extended to use larger jet radii or full event information to incorporate opposite-side and same-side fragmentation details.

The authors remain modest, noting that the current results are preliminary and that distinguishing physical anomalies from detector effects or reconstruction failures requires further calibration, larger datasets, and access to complete event records (including detector hits). They position this work as a foundational step toward data-driven strategies for probing BSM physics in heavy-flavour decays.

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