Energy Dependence of Elliptic Flow Ratio v₂^PP/v₂^RP in Heavy-ion Collisions Using the AMPT Model

Abstract We present a systematic study of the elliptic flow v₂ relative to the participant plane (PP) and reaction plane (RP) in Au+Au collisions at s₍₍ = 7. 7--200 GeV using the AMPT model with the string melting version. The ratio v₂^PP/v₂^RP is investigated under different hadronic cascade times (0. 6 fm/c, 10 fm/c, and the maximum evolution time) and across various collision centralities. The results show that, at a fixed collision energy, the ratio exhibits negligible sensitivity to the duration of the hadronic rescattering stage, indicating that hadronic interactions have little effect on the relative difference generated by initial-state fluctuations. However, a strong energy dependence is observed, the ratio increases with beam energy and saturates above s₍₍ 62. 4 GeV, a trend that persists across all centralities. These findings highlight the dominant role of the partonic phase in converting initial-state geometry fluctuations into final-state momentum anisotropy, and suggest that the system's capacity to perserve the initial geometry weakens at lower energies. Therefore, the ratio v₂^PP/v₂^RP provides a sensitive probe of the interplay between initial-state fluctuations and the dynamical evolution of the medium.