Calculating centrality variables and geometric quantities associated with high energy Pb+Pb and Au+Au collisions using a Monte Carlo Glauber model

The Glauber model provides insight into the initial state of nuclear collisions by treating them in terms of the interactions between their constituent nucleons, in accordance with theories about the scattering of composite particles. These phenomenological techniques are commonly used to determine various geometric quantities associated with such complex, femtoscopic many-body systems. The Monte Carlo Glauber approach uses a random impact parameter and measured nuclear densities to investigate quantifiable properties like particle multiplicity and average geometric eccentricity for heavy ion collisions. The former involves incorporating a particle production model to plot the total transverse energy or the number of particles produced at mid-rapidity, both being measures of centrality. The latter delves into the eccentricity of different event classes, which can be used to characterize various collision shapes for measurements of elliptic flow of heavy mesons. The results of both applications are then compared with analyses from CMS and STAR as part of efforts to study the properties of the ultra-hot, super-dense phase of matter known as the Quark-Gluon Plasma