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Which is the best metric for the space of collider events? Motivated by thesuccess of the Energy Mover's Distance in characterizing collider events, weexplore the larger space of unbalanced optimal transport distances, of whichthe Energy Mover's Distance is a particular case. Geometric and computationalconsiderations favor an unbalanced optimal transport distance known as theHellinger-Kantorovich distance, which possesses a Riemannian structure thatlends itself to efficient linearization. We develop the particle linearizedunbalanced Optimal Transport (pluOT) framework for collider events based on thelinearized Hellinger-Kantorovich distance and demonstrate its efficacy inboosted jet tagging. This provides a flexible and computationally efficientoptimal transport framework ideally suited for collider physics applications.

Which Metric on the Space of Collider Events?