Long-range transverse momentum correlations and radial flow in Pb$-$Pb collisions at the LHC

This Letter presents measurements of long-range transverse-momentum correlations using a new observable, $v_{0}(p_\mathrm{T})$, which serves as a probe of radial flow and medium properties in heavy-ion collisions. Results are reported for inclusive charged particles, pions, kaons, and protons across various centrality intervals in Pb$-$Pb collisions at $\sqrt{s_\mathrm{NN}} = 5.02$ TeV, recorded by the ALICE detector. A pseudorapidity-gap technique, similar to that used in anisotropic-flow studies, is employed to suppress short-range correlations. At low $p_\mathrm{T}$, a characteristic mass ordering consistent with hydrodynamic collective flow is observed. At higher $p_\mathrm{T}$ ($> 3$ GeV/$c$), protons exhibit larger $v_{0}(p_\mathrm{T})$ than pions and kaons, in agreement with expectations from quark-recombination models. These results are sensitive to the bulk viscosity and the equation of state of the QCD medium formed in heavy-ion collisions.