Relating centrality to impact parameter in nucleus-nucleus collisions

Abstract

In ultrarelativistic heavy-ion experiments, one estimates the centrality of a collision by using a single observable, say n, typically given by the transverse energy or the number of tracks observed in a dedicated detector. The correlation between n and the impact parameter b of the collision is then inferred by fitting a specific model of the collision dynamics, such as the Glauber model, to experimental data. The goal of this paper is to assess precisely which information about b can be extracted from data without any specific model of the collision. Under the sole assumption that the probability distribution of n for a fixed b is Gaussian, we show that the probability distribution of the impact parameter in a narrow centrality bin can be accurately reconstructed up to 5% centrality. We apply our methodology to data from the Relativistic Heavy Ion Collider and the Large Hadron Collider. We propose a simple measure of the precision of the centrality determination, which can be used to compare different experiments.