Energy flow polynomials: A complete linear basis for jet substructure

TL;DR

This paper introduces energy flow polynomials as a complete, linear basis for jet substructure observables, enabling efficient computation and systematic analysis of jet properties with applications in particle tagging.

Contribution

The paper presents a novel complete basis of jet observables called energy flow polynomials, with a graph-theoretic representation and demonstrated effectiveness in jet tagging tasks.

Findings

Energy flow polynomials form a complete linear basis for jet observables.

Efficient algorithms are developed for computing energy flow polynomials.

Linear classification using these polynomials achieves high accuracy in jet tagging.

Abstract

We introduce the energy flow polynomials: a complete set of jet substructure observables which form a discrete linear basis for all infrared- and collinear-safe observables. Energy flow polynomials are multiparticle energy correlators with specific angular structures that are a direct consequence of infrared and collinear safety. We establish a powerful graph-theoretic representation of the energy flow polynomials which allows us to design efficient algorithms for their computation. Many common jet observables are exact linear combinations of energy flow polynomials, and we demonstrate the linear spanning nature of the energy flow basis by performing regression for several common jet observables. Using linear classification with energy flow polynomials, we achieve excellent performance on three representative jet tagging problems: quark/gluon discrimination, boosted W tagging, and boosted top tagging. The energy flow basis provides a systematic framework for complete investigations of jet substructure using linear methods.