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.Comment: 17 pages, 5 figures, 3 table