Comparison of Methods for Extracting Three-Dimensional Lévy Source Parameters in √sNN = 200 GeV Au+Au Collisions with EPOS3

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 √sNN = 200 GeV: direct fits to the pair-source distribution D(ρ), and fits to the two-particle correlation function C(q) obtained via (i) the CRAB package, (ii) direct numerical integration of D(ρ), and (iii) fast Fourier transformation (FFT). On an identical momentum grid, numerical integration and FFT are analytically identical and numerically equivalent (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--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 ~ 7--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 $α$.