Comparison of Methods for Extracting Three-Dimensional Lévy Source Parameters in $\sqrt{s_{\text{NN}}} = 200\text{ GeV}$ Au+Au Collisions with EPOS3

Abstract

Bose--Einstein femtoscopy probes the spatiotemporal geometry of the particle-emitting source in heavy-ion collisions, where experimental data favor a Lévy-stable source description. We compare four approaches for extracting 3D Lévy source parameters using $π^+π^+$ pairs from EPOS3-simulated Au+Au collisions at $\sqrt{s_{\text{NN}}} = 200\text{ GeV}$: direct fits to the pair-source distribution $D(\boldsymbolρ)$, and fits to the two-particle correlation function $C(\boldsymbol{q})$ obtained via (i) the CRAB package, (ii) direct numerical integration of $D(\boldsymbolρ)$, and (iii) fast Fourier transformation (FFT). On an identical momentum grid, numerical integration and FFT are analytically identical and numerically equivalent ($\text{RMSE} < 10^{-14}$), while FFT reduces the computation time from hours to seconds. We extract the transverse-mass dependence of the Lévy radii, Lévy index $α$, and correlation strength $λ$ in $0\text{--}10\,\%$ central collisions. All methods reproduce the same physical trends, but CRAB results fluctuate due to event pooling, and correlation-function fits deviate systematically from direct source fits, e.g., with $\sim 7\text{--}9\,\%$ lower $α$. These deviations may reflect residual non-Lévy features of the source, probed differently in coordinate and momentum space, and the comparison of event-averaged parameters with fits to the ensemble-accumulated source, a mixture of Lévy distributions with lower effective $α$.