Limitation of multi-particle correlations for studying the event-by-event distribution of harmonic flow in heavy-ion collisions

TL;DR

This paper analyzes the limitations of using multi-particle cumulants to study event-by-event harmonic flow distributions in heavy-ion collisions, highlighting their insensitivity for narrow distributions and potential issues for broad ones.

Contribution

It demonstrates the limitations of multi-particle cumulants in accurately capturing flow distributions, advocating for data-driven unfolding methods as a better alternative.

Findings

Cumulants are insensitive for narrow flow distributions.

Higher-order cumulants can become ill-defined for broad distributions.

Sign changes in cumulant estimates can occur without non-flow effects.

Abstract

The sensitivity of flow harmonics from cumulants on the event-by-event flow distribution $p(v_n)$ is investigated using a simple central moment expansion approach. For narrow distribution whose width is much smaller than the mean $\sigma_n\ll < v_n >$, the difference between the first three higher-order cumulant estimates $v_n\{4\}$, $v_n\{6\}$ and $v_n\{8\}$ are not very sensitive to the shape of $p(v_n)$. For broad distribution $\sigma_n\gtrsim < v_n >$, the higher-order cumulant estimates differ from each other but may change sign and become ill-defined. This sign change arises from the choice of $p(v_n)$, without the need to invoke non-flow effects. Direct extraction of $p(v_n)$ via a data-driven unfolding method is a more preferred approach for flow distribution measurement.