Sources of Radial-Flow Fluctuations in the Quark-Gluon Plasma

The differential radial flow fluctuation v_{0}(p_{T}) has emerged as a new probe of the quark-gluon plasma. However, its characteristic rise-and-fall pattern with p_{T}, resembling anisotropic flow, remains unexplained. I introduce a momentum rescaling framework that factorizes v_{0}(p_{T}) into kinematic and dynamical components: v_{0}(p_{T})/v_{0}=-[dln⟨n(p_{T})⟩/dlnp_{T}+1]×g(p_{T}). The first factor, determined by spectral shape, generates the rise-and-fall pattern as the spectra transition from exponential to power-law behavior. The dynamical component g(p_{T}) isolates p_{T}-dependent dynamics: <1 signals suppressed fluctuations, >1 indicates enhancement. Analysis of LHC data reveals g(p_{T}) deviates from unity by 20%-40% in central collisions. Predictions for RHIC show that spectral shape alone generates the rise-and-fall baseline pattern with substantial energy dependence. This framework enables tighter medium property constraints by separating kinematic from dynamical effects, with broad applications to anisotropic flow and higher-order radial flow fluctuations.