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.
Highlights
Jet substructure is the analysis of radiation patterns and particle distributions within the collimated sprays of particles emerging from high-energy collisions [1,2,3,4,5]
energy flow polynomials (EFPs) are a special case of C-correlators [74], so not surprisingly, we find a close relationship between EFPs and other classes of observables that are themselves C-correlators, including jet mass, energy correlation functions (ECFs) [51], certain generalized angularities [75], and energy distribution moments [49]
For the dense neural networks (DNNs), we use an architecture consisting of three dense layers of 100 units each connected to a 2-unit softmax output layer, with rectified linear unit (ReLU) activation functions applied to the output of each internal layer
Summary
Jet substructure is the analysis of radiation patterns and particle distributions within the collimated sprays of particles (jets) emerging from high-energy collisions [1,2,3,4,5]. Linear classification with EFPs performs comparably to multivariate machine learning techniques, such as jet images with convolutional neural networks (CNNs) [50, 63,64,65,66] or dense neural networks (DNNs) with a complete set of N -subjettiness observables [57]. Both the linear regression and classification models have few or no hyperparameters, illustrating the power and simplicity of linear learning methods combined with our fully general linear basis for IRC-safe jet substructure. A review of C-correlators and additional tagging plots are left to the appendices
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