Hypergraph-based decay analysis for predicting and classifying states beyond regge trajectories

Regge trajectories provide a simple geometric picture of hadron spectra, but particles at higher-spin and missing states often scatter from linear fits, raising questions about both experimental completeness and theoretical limits of the model. Here, we develop a unified data framework that integrates standard particle listings with hypergraph-based decay features, enabling systematic comparison across baryons and mesons. We employed orthogonal distance regression with bootstrap resampling to quantify uncertainties in slope and intercept estimates, while hypergraph-derived structural invariants (community purity, motif z-scores, and product entropy) serve as quantitative predictors of spectroscopic regularity, establishing decay topology as a microscopic determinant of macroscopic Regge behavior. Applying this hybrid approach to 20 Δ baryon resonances, we obtain strong linear correlation ( R 2 = 0.90) with slope α ′ = 1.53 ± 0.03 GeV −2 , though elevated scatter ( χ 2 / dof = 18.5 ) correlates strongly with resonance width ( r = 0.88, p < 0.001). While hypergraph features did not significantly improve explanatory power beyond quality controls in this pilot dataset ( Δ R 2 = 0.03 , p = 0.42), we introduce a hypergraph-informed confidence framework for missing resonance predictions, where structural decay coherence provides quantitative reliability metrics beyond traditional trajectory extrapolation. Together, these results demonstrate how combining trajectory analysis with network-inspired methods can improve hadron classification and provide concrete predictions for future experimental searches.