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.

Jet substructure at the Large Hadron Collider: A review of recent advances in theory and machine learning

“…Determining the median jet axis is closely related to optimal transport theory [240,241,242,243,244,245,246,247,248] for jet physics in two dimensions, which has recently seen a burst of interest (see, e.g., Refs. [249,250,251,252,253]). 11 Is there another way to proceed to define an approximate median jet axis, that is computationally simple yet is insensitive to recoil?…”