Which Metric on the Space of Collider Events?

TL;DR

This paper investigates the optimal metric for collider event spaces, proposing the Hellinger-Kantorovich distance and a particle linearized unbalanced optimal transport framework, demonstrating its effectiveness in boosted jet tagging.

Contribution

It introduces the particle linearized unbalanced optimal transport framework based on the Hellinger-Kantorovich distance for collider physics, enhancing computational efficiency and flexibility.

Findings

Hellinger-Kantorovich distance is well-suited for collider event analysis.

The pluOT framework improves boosted jet tagging performance.

The proposed method offers a computationally efficient solution for collider physics applications.

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.