Measurement of the longitudinal flow-plane decorrelation using multi-plane cumulants in $\sqrt{s_{{}_{\mathrm{NN}}}}$ = 200 GeV Au+Au, Ru+Ru, and Zr+Zr collisions

Abstract

Measurements of the variation of anisotropic flow-plane angles ($\hat{I}{¨}_n$) with rapidity, commonly known as the flow-plane decorrelation, provide important insights into the initial conditions of the matter produced in heavy-ion collisions. In this paper, using data collected by the STAR experiment, we report the first measurement of the four-plane correlator observable $T_n\{ba;dc\}=⟨⟨\sin [n(\hat{I}{¨}_n^b-\hat{I}{¨}_n^a)]\sin [n(\hat{I}{¨}_n^d-\hat{I}{¨}_n^c)]⟩⟩$, where superscripts $a$, $b$, $c$, and $d$ denote sequential pseudorapidity ($\hat{I}\cdot$) regions with $a$ corresponding to the most backward region, $b$ and $c$ close to mid-rapidity with $\hat{I}{\cdot }_b<0$ and $\hat{I}{\cdot }_c>0$, and $d$ being the most forward. The measurement is performed for the elliptic and triangular flow (i.e. $n=2$ and $3$) in Au+Au and isobar (Ru+Ru, Zr+Zr) collisions at $\sqrt{s_{{}_{\mathrm{NN}}}}$ = 200 GeV. The goal of calculating the correlation of the flow-plane angle variations from backward to mid-central, and from mid-central to forward regions, is to probe the systematic variation of flow angle over a wide $\hat{I}\cdot$ range. In mid-central collisions ($10-30\%$ centrality), we find $T_2\{ba;dc\}=-0.004\pm 0.001(\mathrm{stat})\pm 0.002(\mathrm{syst})$ independent of the collision system. Such a small value of $T_2$ favors a ''random-walk'' variation of the flow-plane angles, where the rapidity correlation length is smaller than the entire region under study. These measurements provide new information on the decorrelation patterns in the system and offer a quantitative estimate of possible systematic variations in anisotropic flow angles such as ''twist'' between forward and backward regions. This opens new opportunities for understanding the three-dimensional structure and the time evolution of the quark-gluon plasma created in heavy-ion collisions.

With updated texts and equations ( 12 pages, 18 figures )