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Decorrelation of neural networks from particle lifetimes in the LHCb topological $b$ trigger

This paper introduces and evaluates two methods to decorrelate neural network scores from $b$ -hadron lifetimes in the LHCb topological trigger, addressing biases caused by misassociated decay products in high-pileup environments to ensure unbiased event selection for physics analyses.

Original authors: Johannes Albrecht, Alessandro Bertolin, James Connaughton, Jonathan Davies, Blaise Delaney, Agnieszka Dziurda, Conor Fitzpatrick, Maciej Giza, Vava V. Gligorov, James A. Gooding, Nicole Schulte, Nicol

Published 2026-07-27

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Johannes Albrecht, Alessandro Bertolin, James Connaughton, Jonathan Davies, Blaise Delaney, Agnieszka Dziurda, Conor Fitzpatrick, Maciej Giza, Vava V. Gligorov, James A. Gooding, Nicole Schulte, Nicole Skidmore, Mika Vesterinen, Mike Williams, Shunan Zhang, Valeriia Zhovkovska

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

Imagine a giant, high-speed camera trying to take a picture of a firework exploding in a crowded stadium. The camera is so fast it can freeze the split-second when the firework bursts, but the stadium is so packed that thousands of other fireworks are going off at the exact same time. This is the challenge facing the LHCb experiment at the Large Hadron Collider. Scientists use this machine to study "beauty" particles (or b-hadrons), which are heavy, unstable particles that decay, or break apart, very quickly. To find them, the computer system acts like a super-fast bouncer at a club, scanning millions of collisions every second to decide which ones are interesting enough to save for later.

The problem is that these beauty particles have a specific "personality": they travel a tiny but measurable distance before they break apart, creating a distinct pattern of debris. The computer uses a smart algorithm, a type of artificial intelligence called a neural network, to spot this pattern. However, in the current, busier version of the experiment, the stadium is so crowded that the bouncer sometimes gets confused. It might accidentally mix up debris from one firework with debris from a neighbor, creating a fake pattern that looks like a long-lived beauty particle. If the computer gets too good at spotting these fakes, it might start ignoring the real, long-lived particles it's supposed to find, ruining the science. This paper explores how to teach the computer to stop making that mistake without losing its ability to find the real fireworks.

The Busy Bouncer and the Fake Clues

The LHCb experiment is designed to study heavy particles that contain a "beauty" quark. These particles are special because they live just long enough to travel about a centimeter before they decay. This creates a unique signature: a "secondary vertex," or a second meeting point for the particles, that is slightly separated from where they were born. To catch these events, the LHCb trigger system uses a machine learning tool called a monotonic Lipschitz neural network (MLNN). Think of this neural network as a highly trained detective who looks at the clues (like how far the particles traveled and how fast they were moving) and gives every event a score. If the score is high enough, the event is saved.

The detective is trained to be "monotonic," meaning that if a particle travels further or has more momentum, the score should go up. This makes sense because real beauty particles usually travel further than the background noise. However, the experiment recently got much busier. In the past, there was roughly one collision per moment (µ = 1.1), but now there are about 5.3 collisions happening at once (µ = 5.3). This is like the bouncer trying to sort through five different parties happening in the same room simultaneously.

Because of this crowd, the detective sometimes gets tricked. It might take a track from one collision and a track from another, combine them, and create a "composite" particle that looks like it traveled a very long distance. This is a "lifetime-correlated background." It's a fake clue that looks exactly like the long-lived beauty particles the scientists want to study. The danger is that the neural network, seeing these fake long-distance tracks, might learn to be suspicious of all long-distance tracks. It might start penalizing real, long-lived beauty particles just because they look a bit like the fakes. This would create a bias, making the experiment less sensitive to the very particles it needs to study.

Teaching the Detective to Ignore the Crowd

To fix this, the authors of the paper tried to "decorrelate" the neural network. In plain English, they wanted to teach the AI that its score should not depend on how long the particle lived, especially for the long-lived ones. They tested two different methods to add a "penalty" to the AI's training process if it started caring too much about the lifetime.

The first method was called DisCo (Distance Correlation). Imagine this as a strict teacher who yells at the student every time their grade changes based on the student's height. If the AI gives a higher score to a long-lived particle, the penalty kicks in to tell it, "No, the score shouldn't change just because the lifetime changed."

The second method was called MoDe (Moment Decomposition). This is a bit more like a flexible coach. Instead of just yelling, the coach breaks down the student's performance into different shapes (mathematical curves) and only penalizes the parts that shouldn't be there. It allows the AI to have a sharp "turn-on" at the beginning (to reject obvious junk) but forces it to stay flat and consistent for the long-lived particles.

The Results: A Flatter, Fairer Score

The team trained their AI models using these two methods and tested them on simulated data, specifically looking at how well they could find real beauty particles like $B^+ \to J/\psi(\mu^+\mu^-)K^+$ and $B^0 \to D^-(K^+\pi^-\pi^-)\pi^+$ .

They found that both methods helped, but they worked in different ways. The DisCo method made the AI less picky about intermediate lifetimes, which kept the score flat for long lifetimes, but it did lower the overall efficiency a bit. The MoDe method, however, was the star of the show. It managed to keep the efficiency high for particles with intermediate lifetimes while still making the score flat for the long-lived ones.

When they looked at the data for particles with lifetimes greater than 4 picoseconds (a picosecond is one-trillionth of a second), the difference was clear. Without any help, the AI's efficiency dropped sharply as the lifetime increased, with a slope of about -24.9. The DisCo method improved this to -12.9, but the MoDe method with a penalty strength of $\lambda = 0.2$ brought the slope down to nearly zero (-6.6 for 3-body candidates). This means the AI was no longer discriminating against the long-lived particles it was supposed to find.

Conclusion

The paper concludes that the busy conditions of the LHC's Run 3 have created a new kind of background noise that confuses the trigger system. By using the MoDe approach to decorrelate the neural network from particle lifetimes, the LHCb experiment can ensure that its "bouncer" remains fair. It will continue to let in the real, long-lived beauty particles without being tricked by the fake, mixed-up tracks from the crowded stadium. This ensures that future scientific studies, which rely on measuring how these particles decay over time, won't be biased by the computer's own confusion. The authors suggest that this method is a robust solution for keeping the data clean and the physics accurate.

Technical Summary: Decorrelation of Neural Networks from Particle Lifetimes in the LHCb Topological b Trigger

Problem Statement
The LHCb experiment's topological beauty (b) trigger is a critical machine learning (ML) component designed to select collision events containing $b$ -hadrons based on their distinct decay topology, specifically large lifetimes and transverse momentum. In Run 3 of the Large Hadron Collider (LHC), the average number of visible proton-proton collisions per bunch crossing ( $\mu$ ) increased from 1.1 (Runs 1 and 2) to 5.3. This higher pile-up environment introduces a specific background mechanism: the misassociation of decay products from different primary vertices (PVs).

When tracks from different PVs are incorrectly combined to form a candidate vertex, the resulting secondary vertex (SV) can exhibit artificially large flight distances and lifetimes. This "lifetime-correlated background" creates a bias where the neural network (NN) scores, which are trained to identify $b$ -decay topologies, inadvertently penalize candidates with large true lifetimes. Consequently, the selection efficiency drops at large lifetimes, introducing a bias that compromises time-dependent physics analyses, which rely on an unbiased response to accurately reconstruct the $b$ -hadron decay-time distribution.

Methodology
To address this, the authors implemented two distinct approaches to decorrelate the monotonic Lipschitz neural networks (MLNNs) used in the trigger from the candidate lifetime ( $\tau$ ) at large decay times. The MLNNs, which select 2- and 3-body candidates, are required to be monotonic in features like transverse momentum ( $p_T$ ) and impact parameter quality ( $\chi^2_{IP}$ ), but they do not explicitly access the lifetime variable.

The study evaluates two penalty terms added to the binary cross-entropy (BCE) loss function during training:

Distance Correlation (DisCo): This method adds a penalty term based on the distance covariance between the NN score ( $\hat{y}$ ) and the lifetime ( $\tau$ ). The penalty is normalized by the self-covariances of the score and lifetime, effectively minimizing the distance correlation ($dCorr$) between the two variables.
Moment Decomposition (MoDe): This approach decomposes the cumulative density function (CDF) of the NN scores, binned by lifetime, into Legendre polynomials. The loss function penalizes the difference between the actual CDF and the decomposition (specifically using a quadratic term, $\ell=2$ ). This allows for a controlled quadratic dependence between $\tau$ and $\hat{y}$ , enforcing monotonicity at large lifetimes while permitting the necessary "turn-on" curve at small lifetimes to reject prompt backgrounds.

The models were trained on simulated samples of $B^+ \to J/\psi(\mu^+\mu^-)K^+$ and $B^0 \to D^-(K^+\pi^-\pi^-)\pi^+$ decays, with background modeled via minimum bias simulations.

Key Contributions and Results
The paper presents the implementation and evaluation of these decorrelation techniques within the LHCb Run 3 topological $b$ trigger framework.

Optimization: The optimal decorrelation strength was found to be $\lambda = 0.8$ for the DisCo approach and $\lambda = 0.2$ for the MoDe approach.
Efficiency Performance: Both methods successfully flattened the selection efficiency at large lifetimes ( $\tau \gtrsim 5$ $τ ≳ 5$ ps), mitigating the efficiency drop observed in non-decorrelated models.
- The DisCo approach achieved a flatter efficiency by reducing the efficiency at intermediate lifetimes and maintaining that lower level at large lifetimes.
- The MoDe approach improved efficiency at large lifetimes while maintaining performance at intermediate lifetimes. This is attributed to the MoDe formulation not penalizing the sharp turn-on curve required at small decay times.
Quantitative Analysis: Linear least-squares regression fits to the efficiency of $B^0$ candidates for $\tau > 4$ ps demonstrated that MoDe provided a superior reduction in the negative slope of the efficiency curve. For 3-body candidates, the MoDe slope was nearly consistent with zero ( $-6.6 \pm 5.5$ ns $^{-1}$ ), compared to the non-decorrelated slope of $-22.2 \pm 2.8$ ns $^{-1}$ .

Significance
The paper concludes that the MoDe approach is better suited for achieving lifetime decorrelation in the topological $b$ trigger. By successfully mitigating the bias introduced by pile-up-induced misassociation without significantly compromising the overall classification power, these methods ensure that the trigger response remains unbiased with respect to particle lifetime. This is essential for preserving the sensitivity of time-dependent measurements in the high-pile-up environment of LHCb Run 3.

The Busy Bouncer and the Fake Clues

Teaching the Detective to Ignore the Crowd

The Results: A Flatter, Fairer Score

Conclusion

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