Relation of hard and total cross sections to centrality

TL;DR

This paper investigates how hard and total cross sections relate to collision centrality by analyzing impact parameters, using charm quark production as a specific example to quantify the fractions involved.

Contribution

It introduces a method to connect impact parameters with cross section fractions, specifically applying this to charm quark production to clarify centrality dependence.

Findings

Hard and geometric cross sections vary with impact parameter.

Impact parameter definitions influence the fraction of hard cross sections.

Charm quark production exemplifies the impact of centrality cuts.

Abstract

We compare the fractions of the hard and geometric cross sections as a function of impact parameter. For a given definition of central collisions, we calculate the corresponding impact parameter and the fraction of the hard cross section contained within this cut. We use charm quark production as a definite example.