Sources of Radial Flow Fluctuations in the Quark-Gluon Plasma

The differential radial flow fluctuation $v_0(p_{\mathrm{T}})$ has emerged as a new probe of the quark-gluon plasma. However, its characteristic rise-and-fall pattern with $p_{\mathrm{T}}$, resembling anisotropic flow, remains unexplained. I introduce a momentum rescaling framework that factorizes $v_0(p_{\mathrm{T}})$ into kinematic and dynamical components: $v_0(p_{\mathrm{T}})/v_0 = -[d\ln\langle n(p_{\mathrm{T}})\rangle/d\ln p_{\mathrm{T}} + 1] \times g(p_{\mathrm{T}})$. 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 $g(p_{\mathrm{T}})$ isolates $p_{\mathrm{T}}$-dependent dynamics: $<1$ signals suppressed fluctuations, $>1$ indicates enhancement. Analysis of LHC data reveals $g(p_{\mathrm{T}})$ 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.