Anisotropy scaling functions in heavy-ion collisions: Insights into the ultracentral flow puzzle and constraints on transport coefficients and nuclear deformation

Anisotropy scaling functions derived from comprehensive 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, Xe+Xe collisions at 5.44 TeV, and Au+Au collisions at 0.2 TeV offer new insights into the ultracentral flow puzzle. These functions integrate diverse measurements into a single curve, clarifying anisotropy attenuation throughout the entire pT and centrality range. They reveal the influence of initial-state eccentricities (ɛn), dimensionless size (R), radial flow, viscous correction to the thermal distribution function (δf), the medium's stopping power (q ), and specific shear viscosity (η/s) on the observed anisotropies. This analysis not only enhances understanding of transport coefficients but also provides crucial constraints on nuclear deformation.