System-size and beam energy dependence of the space-time extent of the pion emission source

Two-pion interferometry measurements are used to extract the Gaussian source radii $R_{out}$, $R_{side}$ and $R_{long}$, of the pion emission sources produced in $d+$Au, Cu$+$Cu and Au$+$Au collisions for several beam collision energies at PHENIX experiment. The extracted radii, which are compared to recent STAR and ALICE data, show characteristic scaling patterns as a function of the initial transverse geometric size of the collision system, and the transverse mass of the emitted pion pairs. These scaling patterns indicate a linear dependence of $R_{side}$ on the initial transverse size, as well as a smaller freeze-out size for the $d+$Au system. Mathematical combinations of the extracted radii generally associated with the emission source duration and expansion rate exhibit non-monotonic behavior, suggesting a change in the expansion dynamics over this beam energy range.