PhyGHT: Physics-Guided HyperGraph Transformer for Signal Purification at the HL-LHC

The High-Luminosity Large Hadron Collider (HL-LHC) at CERN will produce unprecedented datasets capable of revealing fundamental properties of the universe. However, realizing its discovery potential faces a significant challenge: extracting small signal fractions from overwhelming backgrounds dominated by approximately 200 simultaneous pileup collisions. This extreme noise severely distorts the physical observables required for accurate reconstruction. To address this, we introduce the Physics-Guided Hypergraph Transformer (PhyGHT), a hybrid architecture that combines distance-aware local graph attention with global self-attention to mirror the physical topology of particle showers formed in proton-proton collisions. Crucially, we integrate a Pileup Suppression Gate (PSG), an interpretable, physics-constrained mechanism that explicitly learns to filter soft noise prior to hypergraph aggregation. To validate our approach, we release a novel simulated dataset of top-quark pair production to model extreme pileup conditions. PhyGHT outperforms state-of-the-art baselines from the ATLAS and CMS experiments in predicting the signal's energy and mass correction factors. By accurately reconstructing the top quark's invariant mass, we demonstrate how machine learning innovation and interdisciplinary collaboration can directly advance scientific discovery at the frontiers of experimental physics and enhance the HL-LHC's discovery potential. The dataset and code are available at https://github.com/rAIson-Lab/PhyGHT