Azimuthal Anisotropy Scaling for Identified Mesons and Baryons: Insights into Medium Transport Properties, Equation of State and Hadronic Re-scattering

Species-resolved azimuthal anisotropy scaling functions are constructed from measurements of v2(pT , cent) and v3(pT , cent) for identified mesons and baryons over a broad pT range in Pb+Pb ( √sNN = 2.76 and 5.02 TeV) and Xe+Xe (5.44 TeV) collisions at the LHC, and in U+U, Au+Au, Cu+Au, and Cu+Cu collisions at top RHIC energy. The scaling functions exhibit robust data collapse across centralities and collision systems, extending from the low-pT collective regime into the high-pT quenching-dominated region. Simultaneous intra-harmonic scaling and inter-harmonic mapping separate geometric inputs from response coefficients associated with attenuation, radial flow, and late-stage hadronic re-scattering. The constrained coefficients exhibit distinct trends: kβ varies primarily with beam energy and attenuation conditions, ζrf evolves strongly with centrality and multiplicity while retaining additional system and beam-energy dependence, and ζhs is negligible for the LHC cases studied but finite for the RHIC systems. These trends substantially restrict interchangeability among the response coefficients and provide complementary sensitivity to viscous attenuation, partonic energy loss, collective expansion, and hadronic dynamics. The evolution of ζrf also provides sensitivity to the equation of state, while geometry-sensitive inter-harmonic scaling provides system-consistent constraints on intrinsic quadrupole deformation, yielding preferred values of β2 ≈ 0.18 for Xe and β2 ≈ 0.20 for U. These results establish species-resolved anisotropy scaling as a quantitative, data-driven framework for charting QGP response and nuclear geometry.