Which Metric on the Space of Collider Events?

Abstract

Which is the best metric for the space of collider events? Motivated by the success of the Energy Mover's Distance in characterizing collider events, we explore the larger space of unbalanced optimal transport distances, of which the Energy Mover's Distance is a particular case. Geometric and computational considerations favor an unbalanced optimal transport distance known as the Hellinger-Kantorovich distance, which possesses a Riemannian structure that lends itself to efficient linearization. We develop the particle linearized unbalanced Optimal Transport (pluOT) framework for collider events based on the linearized Hellinger-Kantorovich distance and demonstrate its efficacy in boosted jet tagging. This provides a flexible and computationally efficient optimal transport framework ideally suited for collider physics applications.

17 pages, 5 figures, 3 tables

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• Neural Embedding: Learning the Embedding of the Manifold of Physics Data
• Hyperparameter Optimization of Generative Adversarial Network Models for High-Energy Physics Simulations
• Earth mover's distance as a measure of CP violation
• Pileup and Infrared Radiation Annihilation (PIRANHA): A Paradigm for Continuous Jet Grooming
• A Field Guide to Event-Shape Observables Using Optimal Transport