Anisotropy Scaling Functions in Heavy-Ion Collisions: Insights into the `Ultra-Central Flow Puzzle' and Constraints on Transport Coefficients and Nuclear Deformation

Anisotropy scaling functions, derived from extensive measurements of transverse momentum- and centrality-dependent anisotropy coefficients v₂(pT,cent) and v₃(pT,cent) in Pb+Pb collisions at 5.02 and 2.76 TeV, and Xe+Xe collisions at 5.44 TeV at the LHC, shed light on the 'ultra-central flow puzzle'. These functions amalgamate diverse measurements into a unified curve, elucidating anisotropy attenuation across the full pT and centrality range and unveiling dependencies on key factors including initial-state eccentricities (εₙ), dimensionless size (R), radial flow, viscous correction to the thermal distribution function (δf), the medium's stopping power (q̂), and specific shear viscosity (η/s). Their analysis provides distinct insights into transport coefficients and nucleus deformation constraints.