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

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 $σ_n\ll < v_n >$, 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 $σ_n\gtrsim < v_n >$, 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.

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