A Field Guide to Event-Shape Observables Using Optimal Transport

TL;DR

This paper explores the use of optimal transport to evaluate event-shape observables in collider physics, providing guidance on metric choices to enhance analysis sensitivity and robustness.

Contribution

It introduces a framework using manifold distances based on optimal transport for analyzing collider events, with detailed guidance on metric selection and its impact.

Findings

Optimal transport-based event-shape observables can improve sensitivity to signals.

Choice of metric significantly affects the robustness against non-perturbative effects.

Analytical and simulated studies demonstrate the framework's effectiveness.

Abstract

We lay out the phenomenological behavior of event-shape observables evaluated by solving optimal transport problems between collider events and reference geometries -- which we name 'manifold distances' -- to provide guidance regarding their use in future studies. This discussion considers several choices related to the metric used to quantify these distances. We explore the differences between the various options, using a combination of analytical studies and simulated minimum-bias and multi-jet events. Making judicious choices when defining the metric and reference geometry can improve sensitivity to interesting signal features and reduce sensitivity to non-perturbative effects in QCD. The goal of this article is to provide a 'field guide' that can inform how choices made when defining a manifold distance can be tailored for the analysis at-hand.