Relating centrality to impact parameter in nucleus-nucleus collisions
Sruthy Jyothi Das🇫🇷 · Giuliano Giacalone🇫🇷 · Pierre-Amaury Monard🇫🇷 · Jean-Yves Ollitrault🇫🇷
In ultrarelativistic heavy-ion experiments, one estimates the centrality of a collision by using a single observable, say , typically given by the transverse energy or the number of tracks observed in a dedicated detector. The correlation between and the impact parameter, , 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 can be extracted from data without any specific model of the collision. Under the sole assumption that the probability distribution of for a fixed is Gaussian, we show that the probability distribution of the impact parameter in a narrow centrality bin can be accurately reconstructed up to 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.