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

Abstract: Anisotropy scaling functions derived from comprehensive measurements of transverse momentum- and centrality-dependent anisotropy coefficients (v_2(p_T,\text{cent})) and (v_3(p_T,\text{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 `ultra-central flow puzzle.' These functions integrate diverse measurements into a single curve, clarifying anisotropy attenuation throughout the entire (p_T) and centrality range. They reveal the influence of initial-state eccentricities ((\varepsilon_{n})), dimensionless size ((\mathbb{R})), radial flow, viscous correction to the thermal distribution function ((\delta_f)), the medium's stopping power ((\Hat{q})), and specific shear viscosity ((\eta/s)) on the observed anisotropies. This analysis not only enhances understanding of transport coefficients but also provides crucial constraints on nuclear deformation.