Understanding radial flow fluctuations through event-by-event momentum rescaling

Abstract: The transverse momentum ($p_{\mathrm{T}}$) differential radial flow fluctuation, $v_0(p_{\mathrm{T}})$, has emerged as a new probe of the quark-gluon plasma in heavy-ion collisions. I present a framework that recasts $v_0(p_{\mathrm{T}})$ as a $p_{\mathrm{T}}$-dependent momentum rescaling function $g(p_{\mathrm{T}})$. This transformation reveals that constant rescaling ($g(p_{\mathrm{T}})=1$) alone captures the main features of $v_0(p_{\mathrm{T}})$, including its characteristic rise-and-fall pattern that emerges naturally from the particle spectral shape. Analysis of ATLAS data at $\sqrt{s_{NN}}=5.02$ TeV reveals small but significant deviations of $g(p_{\mathrm{T}})$ from unity with clear centrality dependence. This transformation converts $v_0(p_{\mathrm{T}})$ into a transparent probe of $p_{\mathrm{T}}$-dependent dynamics: $g(p_{\mathrm{T}})<1$ signals suppressed fluctuations while $g(p_{\mathrm{T}})>1$ indicates enhanced fluctuations relative to global radial flow. Predictions for lower energies reveal spectral shape differences alone could generate substantial variations in $v_0(p_{\mathrm{T}})$. This framework enables direct connections between theoretical predictions and underlying physics mechanisms.