The shape of differential radial flow $v_0(p_T)$, not its zero-crossing, carries physical information

Abstract

Radial flow, a key collective phenomenon in heavy-ion collisions, manifests itself through event-by-event fluctuations of transverse-momentum ($p_{\mathrm{T}}$) spectra. The $p_{\mathrm{T}}$-differential radial flow observable, $v_0(p_{\mathrm{T}})$, was introduced to quantify local spectral-shape fluctuations, but it is unavoidably influenced by global multiplicity fluctuations. Using the HIJING model, we show that different event-activity definitions for centrality classification and different spectral normalization schemes generate a constant vertical offset in $v_0(p_{\mathrm{T}})$ without altering its shape. This offset reflects the impact of residual volume/centrality fluctuations rather than genuine dynamical radial flow fluctuations. Accordingly, only the shape of $v_0(p_{\mathrm{T}})$, or equivalently its derivative $dv_0(p_{\mathrm{T}})/dp_{\mathrm{T}}$, carries physical information about radial-flow dynamics; its zero crossing does not. Practical implications include the need to vertically align measurements from different experiments before comparison, thereby removing normalization ambiguities when constraining QGP properties.