An MLE analysis on the relationship between the initial-state granularity and final-state flow factorization

TL;DR

This paper uses maximum likelihood estimation to analyze how initial-state fluctuations influence final-state flow factorization in heavy-ion collisions, highlighting MLE's advantages over traditional methods for sensitive observables.

Contribution

The study introduces MLE as a robust alternative to multi-particle cumulants for analyzing flow factorization sensitive to initial-state fluctuations.

Findings

Flow remains unchanged across different initial conditions.

Harmonic coefficients from MLE and cumulants are consistent.

Flow factorization varies significantly with initial conditions and estimators.

Abstract

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 (IC), is modeled using a peripheral tube model. Besides differential flow, our analysis focuses on a class of more sensitive observables known as flow factorization. Specifically, we evaluate these observables using MLE, an asymptotically normal and unbiased tool in standard statistical inference. Our findings show that the resulting differential flow remains essentially unchanged for different IC defined by the peripheral tube model. The resulting harmonic coefficients obtained using MLE and multi-particle cumulants are found to be consistent. However, the calculated flow factorizations show significant variations depending on both the IC and the estimators, which is attributed to their sensitivity to initial-state fluctuations. Thus, we argue that 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.