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

Abstract

Scaling functions for the centrality and transverse momentum dependence of \(v_2(p_T,\text{cent})\) and \(v_3(p_T,\text{cent})\) are constructed for identified mesons and baryons in Pb+Pb (\(\sqrt{s_{NN}}=2.76,\ 5.02\)~TeV), Xe+Xe (5.44~TeV), and Au+Au (0.2~TeV) collisions. These species-resolved functions capture the interplay of initial geometry, viscous attenuation, radial flow, partonic energy loss, and hadronic re-scattering across both flow- and quenching-dominated regimes. The systematic growth of the radial-flow parameter \(\zeta_{\rm rf}\) with multiplicity and beam energy provides direct empirical constraints on the equation of state (EOS) of hot QCD matter. The extracted parameters also yield differential constraints on the specific shear viscosity \(\eta/s\), the jet-quenching parameter \(\hat{q}\), and late-stage hadronic dynamics. LHC systems exhibit low \(\eta/s\), strong radial flow, and negligible re-scattering at high energy density, whereas Au+Au at RHIC energy shows even lower \(\eta/s\), weaker radial flow, finite re-scattering, and reduced energy density. The coexistence of strong radial flow at low \(p_T\) and significant jet suppression at high \(p_T\) emerges as a defining hallmark of QGP formation, establishing the framework as a quantitative probe of QGP transport properties and EOS stiffness.