Reconstructing the impact parameter of proton-nucleus and nucleus-nucleus collisions

TL;DR

This paper presents a model-independent method to reconstruct the true impact parameter distribution in proton-nucleus and nucleus-nucleus collisions using experimental centrality data, improving accuracy especially for more central collisions.

Contribution

The authors develop a technique to reconstruct impact parameter distributions directly from experimental centrality measures without relying on specific collision models.

Findings

Reconstruction is reliable up to about 10% centrality.

More accurate for nucleus-nucleus than proton-nucleus collisions.

Applied to LHC data to extract impact parameter distributions.

Abstract

In proton-nucleus and nucleus-nucleus collision experiments, one determines the centrality of a collision according to the multiplicity or energy deposited in a detector. This serves as a proxy for the true collision centrality, as defined by the impact parameter. We show that the probability distribution of impact parameter in a given bin of experiment-defined centrality can be reconstructed without assuming any specific model for the collision dynamics, in both proton-nucleus and nucleus-nucleus systems. The reconstruction is reliable up to about 10\% centrality, and is more accurate for nucleus-nucleus collisions. We perform an application of our procedure to experimental data from all the CERN Large Hadron Collider (LHC) collaborations, from which we extract, in Pb+Pb and $p$+Pb collisions, the corresponding distributions of impact parameter.