Flow-plane decorrelations in heavy-ion collisions with multiple-plane cumulants

The azimuthal correlations between local flow planes at different (pseudo)rapidities ($\eta$) may reveal important details of the initial nuclear matter density distributions in heavy-ion collisions. Extensive experimental measurements of a factorization ratio ($r_2$) and its derivative ($F_2$) have shown evidence of the longitudinal flow-plane decorrelation. However, nonflow effects also affect this observable and prevent a quantitative understanding of the phenomenon. In this paper, to distinguish decorrelation and nonflow effects, we propose a new cumulant observable, $T_2$, which largely suppresses nonflow. The technique sensitivity to different initial-state scenarios and nonflow effects are tested with a simple Monte Carlo model, and in the end, the method is applied to events simulated by a multiphase transport model (AMPT) for Au+Au collisions at $\sqrt{s_{\rm NN}} =200$ GeV. We also emphasize that a distinct decorrelation signal requires not only the right sign of an observable, but also its proper dependence on the $\eta$-window of the reference flow plane, to be consistent with the pertinent decorrelation picture.