Elucidating the event-by-event flow fluctuations in heavy-ion collisions via the event shape selection technique

The presence of large event-by-event flow fluctuations in heavy ion collisions at RHIC and the LHC provides an opportunity to study a broad class of flow observables. This paper explores the correlations among harmonic flow coefficients $v_n$ and their phases $\Phi_n$, and the rapidity fluctuation of $v_n$. The study is carried out usin Pb+Pb events generated by the AMPT model with fixed impact parameter. The overall ellipticity/triangularity of events is varied by selecting on the eccentricities $\epsilon_n$ or the magnitudes of the flow vector $q_n$ for n=2 and 3, respectively. The responses of the $v_n$, the event-plane correlations, and the rapidity fluctuations, to the change in $\epsilon_n$ and $q_n$ are then systematized. Strong positive correlations are observed among all even harmonics $v_2, v_4$, and $v_6$ (all increase with $q_2$), between $v_2$ and $v_5$ (both increase with $q_2$) and between $v_3$ and $v_5$ (both increase with $q_3$), consistent with the effects of nonlinear collective response. In contrast, an anti-correlation is observed between $v_2$ and $v_3$ similar to that seen between $\epsilon_2$ and $\epsilon_3$. These correlation patterns are found to be independent of whether selecting on $q_n$ or $\epsilon_n$, validating the ability of $q_n$ in selecting the initial geometry. A forward/backward asymmetry of $v_n(\eta)$ is observed for events selected on $q_n$ but not on $\epsilon_n$, reflecting dynamical fluctuations exposed by the $q_n$ selection. Many event-plane correlators show good agreement between $q_n$ and $\epsilon_n$ selections, suggesting that their variations with $q_n$ are controlled by the change of $\epsilon_n$ in the initial geometry. Hence these correlators may serve as promising observables for disentangling the fluctuations generated in various stages of the evolution of the matter created in heavy ion collisions.