Reconstructing short-lived particles using hypergraph representation learning

Inside the Large Hadron Collider, a massive ring of magnets buried beneath the Swiss-French border, scientists smash protons together at nearly the speed of light. These collisions recreate the searing energy of the universe's first moments, spawning a cascade of new particles. Most of these particles are heavy and incredibly short-lived, decaying almost instantly into a spray of more stable debris. To understand the fundamental laws of nature, physicists must reconstruct the original, fleeting particles from this debris, much like a forensic expert trying to deduce the shape of a shattered vase by examining the scattered shards. The challenge lies in the sheer number of pieces; when heavy particles decay, they often produce up to 20 "jets"—narrow streams of particles that fly out in specific directions. Figuring out which jets came from which parent particle is a puzzle of staggering complexity, especially when the debris includes invisible particles that leave no trace in the detector.

A team of researchers at the University of Manchester has developed a new way to solve this puzzle, one that treats the collision data not as a simple list of particles, but as a complex web of relationships. They call their method HyPER. Instead of looking at particles in isolation or just in pairs, HyPER uses a mathematical structure called a hypergraph to understand how groups of particles are connected all at once. In a standard approach, a computer might try to link particle A to particle B, and then particle B to particle C, building a chain step by step. HyPER, however, can look at a whole group of particles simultaneously and ask, "Do these three specific particles together form a single parent particle?" This shift in perspective allows the system to see patterns that simpler methods miss, particularly in events where the number of particles is very high.

The researchers tested this new system on a specific type of collision where a pair of top quarks—the heaviest known elementary particles—decay entirely into jets. In this scenario, the two top quarks break down into six quarks, which then turn into six jets, plus any extra jets created by the violent collision itself. The goal is to correctly identify which three jets belong to one top quark and which three belong to the other. The team trained their HyPER model on millions of simulated collisions, teaching it to recognize the correct groupings. They then pitted it against two of the most advanced existing methods used by physicists today. The results showed that HyPER was able to correctly reconstruct the parent particles in 67 percent of the events, outperforming the other methods which succeeded in about 65 percent and 64.5 percent of cases.

What makes this achievement particularly significant is not just the slight increase in accuracy, but the efficiency with which it was achieved. The HyPER model is remarkably small, containing roughly 3,450 trainable parameters. In contrast, the competing models require millions of parameters to function. To put this in perspective, the new model contains a factor of 20 fewer parameters than one of the existing tools, yet it delivers better results. This efficiency matters because it means the model is less likely to "overfit," or memorize the training data rather than learning the underlying physics, and it requires far less computing power to run. The researchers found that even when they reduced the amount of training data available, HyPER remained the most accurate tool, suggesting it is robust enough to handle the limited datasets often found in rare physics searches.

The success of HyPER opens the door to studying even more complex and rare events in particle physics. Because the system is designed to handle groups of particles of any size, it could eventually be used to reconstruct particles that decay into four, five, or more jets. While the current study focused on all-hadronic decays where neutrinos are absent, the researchers note that future work aims to extend the method to include the reconstruction of final-state neutrino kinematics. The researchers demonstrated that their approach works well for the specific case of top quark pairs, but the underlying method is flexible enough to be applied to a wide variety of physics processes. By providing a more powerful and efficient way to visualize the relationships between particles, HyPER offers a new tool for peering into the fundamental structure of the universe, helping scientists distinguish the signal of new physics from the background noise of the known world.