Analysis of flow factorization and event-plane correlations based on a maximum likelihood estimator

In this study, we use the maximum likelihood estimator (MLE) to explore factorization and event-plane correlations in relativistic heavy-ion collisions. Our analyses incorporate both numerical simulations and publicly available data from the CMS Collaboration. We focus on Au+Au collisions at 200 GeV and Pb+Pb collisions at 2.76 TeV. The differential flows obtained for various centrality windows and momentum cuts are consistent with conventional methodologies such as multi-particle cumulants and event-plane methods. Leveraging these findings, we proceed to undertake further analysis of flow factorization and event-plane correlations. These quantities are relevant because of their sensitivity to initial-state fluctuations. While higher-order correlators might provide different implementations of factorization ratio, the MLE estimator is readily applied to these scenarios. Moreover, MLE's unique capabilities allow us to compute specific correlators that are typically inaccessible by other means. As an asymptotically normal and unbiased estimator, MLE provides a valuable alternative tool for flow and correlation analysis.