Tracing pT-differential radial flow from blast-wave analytics to quark coalescence

The observable $v_0(\text{pt})$, which quantifies event-by-event fluctuations in the differential transverse-momentum spectrum, is proposed as a direct and penetrating probe of radial flow in heavy-ion collisions. Recent measurements at the LHC exhibit a clear mass ordering for pions, kaons and protons at low \pt and a baryon-meson splitting at intermediate \pt, resembling to the well-known features of elliptic flow ($v_2$). In this letter, we first derive an analytic expression of $v_0(\text{pt})$ within a Blast-Wave framework incorporating fluctuations of freeze-out temperature and radial expansion velocity, which can naturally explains the experimentally observed mass ordering. The distinct dynamical origins of the mass ordering in $v_0(\text{pt})$ and $v_2(\text{pt})$ are discussed. Furthermore, using the AMPT model, we demonstrate that the baryon-meson splitting emerges spontaneously from the quark coalescence. This study provides deeper insight into the $v_0(\text{pt})$ observable and the collective dynamics of the QGP.