Measurement of the longitudinal flow-plane decorrelation using multi-plane cumulants in sqrt(s_NN) = 200 GeV Au+Au, Ru+Ru, and Zr+Zr collisions

Measurements of the variation of anisotropic flow-plane angles (Psi_n) with rapidity, commonly known as 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 cumulant observable T_n{ba;dc} = <<sin[n(Psi_n^b - Psi_n^a)] sin[n(Psi_n^d - Psi_n^c)]>>, where superscripts a, b, c, and d denote sequential regions in pseudorapidity, with a corresponding to the most backward pseudorapidity region. The measurement is performed for elliptic and triangular flow (i.e., n = 2 and 3) in Au+Au and isobar (Ru+Ru, Zr+Zr) collisions at sqrt(s_NN) = 200 GeV. The goal of calculating the correlation of flow-plane angle variations from backward pseudorapidity (eta_a) to mid-pseudorapidity (eta_b) region and from mid-pseudorapidity (eta_c) to forward pseudorapidity (eta_d) region, is to probe the systematic variation of flow angle over a wide pseudorapidity range. In mid-central collisions (10-30 percent centrality), we find T_2{ba;dc} = -0.004 +/- 0.001 (stat) +/- 0.002 (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 pseudorapidity 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 pseudorapidity regions. This opens new opportunities for understanding the three-dimensional structure of the quark-gluon plasma created in heavy-ion collisions.