Study of $p_\mathrm{T}$-differential radial flow in blast-wave model

Abstract: The transverse momentum-differential radial flow observable $v_0(p_\mathrm{T})$, recently proposed and measured by the ATLAS and ALICE collaborations, provides a novel tool to probe radial expansion dynamics in high-energy heavy-ion collisions. In this work, we conduct a detailed study of $v_0(p_\mathrm{T})$ using a blast-wave model that incorporates hydrodynamic-like expansion and thermal emission. We introduce event-by-event fluctuations in the transverse expansion velocity and kinetic freeze-out temperature using Gaussian probability distributions. Our results show that increasing the mean expansion velocity leads to a clear mass ordering in $v_0(p_\mathrm{T})$, while fluctuations in both expansion velocity and freeze-out temperature significantly enhance the magnitude of $v_0(p_\mathrm{T})$, particularly at higher $p_\mathrm{T}$. We fit blast-wave model calculations for identified hadrons ($\pi$, K, and p) to recent ALICE data from Pb--Pb collisions at $\sqrt{s_\mathrm{NN}}$ = 5.02 TeV using a Bayesian parameter estimation framework. The extracted mean transverse expansion velocity decreases, while the kinetic freeze-out temperature increases, from central to peripheral collisions. Additionally, the freeze-out temperatures inferred from $v_0(p_\mathrm{T})$ are systematically higher than those obtained from conventional $p_\mathrm{T}$-spectra fits, likely due to the reduced sensitivity of $v_0(p_\mathrm{T})$ to resonance decay contributions.