Hypergraphs in LHC phenomenology — the next frontier of IRC-safe feature extraction
Partha Konar (Theoretical Physics Division, Physical Research Laboratory, Shree Pannalal Patel Marg, Ahmedabad, Gujarat, 380009, India); Vishal Ngairangbam (Theoretical Physics Division, Physical Research Laboratory, Shree Pannalal Patel Marg, Ahmedabad, Gujarat, 380009, India); Michael Spannowsky (Institute for Particle Physics Phenomenology, Durham University, Durham, DH1 3LE, U.K., Department of Physics, Durham University, Durham, DH1 3LE, U.K.)
In this study, we critically evaluate the approximation capabilities of existing infra-red and collinear (IRC) safe feature extraction algorithms, namely Energy Flow Networks (EFNs) and Energy-weighted Message Passing Networks (EMPNs). Our analysis reveals that these algorithms fall short in extracting features from any N-point correlation that isn’t a power of two, based on the complete basis of IRC safe observables, specifically C-correlators. To address this limitation, we introduce the Hypergraph Energy-weighted Message Passing Networks (H-EMPNs), designed to capture any N-point correlation among particles efficiently. Using the case study of top vs. QCD jets, which holds significant information in its 3-point correlations, we demonstrate that H-EMPNs targeting up to N=3 correlations exhibit superior performance compared to EMPNs focusing on up to N=4 correlations within jet constituents.
