Final-state centrality in relativistic heavy-ion simulations from neural networks

Abstract: Experiments in relativistic heavy-ion collisions determine centrality from final-state quantities, usually the charged-particle multiplicity. Performing the same in hydrodynamic simulations requires millions of events, which is impractical for state-of-the-art hybrid models, and centrality is therefore commonly approximated by the initial entropy or energy. We show that neural networks trained on a few hundred hybrid events predict the event-by-event multiplicity and mean transverse momentum $[p_T]$ with relative errors of 1--2\%, which makes it possible to generate millions of collisions at a small fraction of the cost of the full simulation. For Pb--Pb collisions at $2.76$~TeV and Au--Au collisions at $200$~GeV, the initial-state and final-state definitions select nearly the same events in 10\%-wide classes, but up to 20\% of the events change class when the classes are 1\% wide. We then compute the fluctuations of $[p_T]$ and its Pearson correlations with a proxy of the elliptic flow, estimated from the initial eccentricity, and with multiplicity. The first correlation is insensitive to how centrality is defined, while the second changes substantially. The approach can be applied at every design point of Bayesian analyses at modest additional cost.