MLE analysis of the relationship between the initial-state granularity and final-state flow factorization*

This is the authors' abstract. We don't add key points for this paper.

In this study, we employ the maximum likelihood estimator (MLE) to investigate the relationship between initial-state fluctuations and final-state anisotropies in relativistic heavy-ion collisions. The granularity of the initial state, reflecting fluctuations in the initial conditions (ICs), is modeled using a peripheral tube model. In addition to differential flow, our analysis focuses on a class of more sensitive observables known as flow factorization. Specifically, we evaluate these observables using the MLE, an asymptotically normal and unbiased tool in standard statistical inference. Our findings show that the resulting differential flow remains essentially unchanged for different ICs defined by the peripheral tube model. The resulting harmonic coefficients obtained using the MLE and multi-particle cumulants are found to be consistent. However, the calculated flow factorizations show significant variations depending on both the IC and estimators, which is attributed to their sensitivity to initial-state fluctuations. Thus, we argue that the MLE offers a compelling alternative to standard methods, such as multi-particle correlators, particularly for sensitive observables constructed from higher moments of the azimuthal distribution.