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When two heavy nuclei smash into each other at enormous speeds, they don't collide as whole objects like billiard balls. Only part of their matter comes into contact. How many nucleons (protons and neutrons) actually took part in the collision, and how many flew past, is not known in advance. All subsequent measurements depend on this number, but it cannot be observed directly.

Previously, events were sorted by the number of produced charged particles: many particles meant a head-on collision, few meant a glancing one. But this sorting is crude. Events with the same number of particles can have different numbers of participants. It's like trying to guess the size of a kitchen from the number of guests at a party: sometimes a small room is crowded, and a large one is spacious.

The new method works differently. Instead of assigning each event a single class, it computes the probability for each possible number of participants and binary collisions. This uses a known model of how nuclei overlap and statistics of how many particles are typically produced for a given number of participants. The result is not a hard label but a probability distribution.

This approach removes some of the uncertainty that was previously masked as event "centrality." Now we can honestly say: we don't know the exact number of participants, but we know how likely each value is. It's like going from a black-and-white photo to a grayscale one — details become visible even if the focus isn't perfect.

Original abstract

as written by the authors arXiv:2608.14045v1

We propose the Inference-driven Participant Determination (IPD) method, a Bayesian framework for inferring event-by-event posterior distributions of the number of participants ($$N_{\text{part}}$$) and binary collisions ($$N_{\text{coll}}$$) from final-state charged-particle multiplicities in relativistic heavy-ion collisions. The joint distribution of $$(N_{\text{part}}, N_{\text{coll}})$$ obtained from the Monte-Carlo Glauber model is used as the prior, while negative binomial distributions calibrated to charged-particle multiplicity fluctuations define the likelihood. This approach replaces conventional hard-cut centrality classification with a probabilistic assignment based on $$N_{\text{part}}$$, making the multiplicity--geometry smearing explicit and reducing the impact of volume fluctuations on downstream observables. A closure test using an UrQMD-MCG hybrid model at $$\sqrt{s_{NN}} = 19.6$$~GeV shows that the method yields well-calibrated posterior distributions with negligible bias and improves the reconstruction of net-proton cumulants relative to conventional multiplicity-based centrality selection.