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Collision energy and system size dependence of longitudinal flow decorrelation in heavy-ion collisions at RHIC energies

In heavy-ion collisions, the initial collision geometry and its fluctuations drive the collective expansion of final-state hadrons in the transverse plane. However, longitudinal fluctuations induce event-plane twist and flow magnitude asymmetries, collectively known as longitudinal flow decorrelation. Using a multi-phase transport (AMPT) model, we systematically investigate the dependence of collision energy and system size of this phenomenon with Au+Au collisions at $\sqrt{s_{\mathrm{NN}}}$ = 19.6, 27, 54.4, 200 GeV and isobar collisions (Zr+Zr and Ru+Ru) at $\sqrt{s_{\mathrm{NN}}}$ = 200 GeV. The results reveal two distinct decorrelation components: $r_n(η)$, which includes flow magnitude asymmetry and event-plane twist, and $R_n(η)$ which arises purely from event-plane twist. Both $r_n(η)$ and $R_n(η)$ decrease linearly with $η$ and exhibit a significant dependence on collision energy and the size of the system. Through the slope parameters $F_n$ in the linear parametrization $r_n(η) = 1-2F_nη$, we can quantify the strength of decorrelation. We further observe that both $F_2$ and $F_3$ demonstrate a pronounced power-law scaling behavior with collision energy, following the relation $F_n \propto log \sqrt{s_{NN}}$. These results provide valuable insights into the three-dimensional modeling of the initial stage and the evolution of relativistic heavy-ion collisions.