Hypergraphs in LHC Phenomenology -- The Next Frontier of IRC-Safe Feature Extraction

TL;DR

This paper identifies limitations in existing IRC-safe feature extraction algorithms for particle physics and introduces Hypergraph EMPNs, which effectively capture complex N-point correlations, improving jet classification performance.

Contribution

The paper proposes Hypergraph EMPNs that can extract all N-point correlations, overcoming the limitations of previous methods that only handle powers of two.

Findings

H-EMPNs outperform EMPNs in top vs. QCD jet classification.

H-EMPNs effectively capture 3-point correlations in jet data.

Existing algorithms are limited to N-point correlations that are powers of two.

Abstract

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.