Optimal-Transport Contrastive Learning for Centrality Determination in Heavy-Ion Collisions

Abstract

Determining centrality of heavy-ion collisions with high resolution is essential for event-by-event analyses, in particular for net-proton fluctuation measurements aimed at locating the QCD critical point. Supervised machine-learning approaches rely on labels generated by model and therefore inherit the model dependence of the training target. In this work, we propose an unsupervised method to determine collision centrality based on optimal transport. Each collision is represented by its 1-Wasserstein distances to a fixed set of landmark events chosen to cover the measured multiplicity range. A point-cloud network trained by contrastive learning then compresses these distances into a compact event embedding, which is partitioned into equal-size centrality classes. We find that this approach groups events with similar $N_{\rm part}$ and yields a better centrality resolution, quantified by the normalized width of the $N_{\rm part}$ distribution, than the conventional method of cutting on particle multiplicity. The method, however, encounters a bottleneck once realistic kinematic cuts are applied to the particles. We attribute this degraded performance to the loss of distinct features between central and peripheral collisions because of applying kinematic cuts. The application of optimal transport to centrality determination in experimental data, remains an open problem that needs further study.