Excitation function of femtoscopic Lévy source parameters of pion pairs in EPOS4

Abstract: Three-dimensional (3D) femtoscopic source parameters of pions provide a sensitive probe of the space-time structure of particle-emitting sources in high-energy heavy-ion collisions. Compared to one-dimensional measurements, 3D femtoscopy not only provides a valuable cross-check but also offers a more complete characterization of the source geometry and its dynamical evolution. Particularly, differences between the "out" and "side" directions are sensitive to signals of a strong first-order phase transition, while the collision-energy dependence of Levy radii may reveal non-monotonic features related to the equation of state (EoS). In this work, we systematically investigate the transverse mass and collision-energy dependence of the three-dimensional femtoscopic parameters of pion pairs with Levy-type sources in the STAR Beam Energy Scan (BES) range from $\sqrt{s_{NN}} = 7.7$ to $200$ GeV using the EPOS4 model. The analyzed parameters include the Levy index $α$, the correlation strength $λ$, and the three-dimensional radii $R_{\rm {out}}$, $R_{\rm side}$ and $R_{\rm long}$ , derived quantities such as the radius difference $R_{\rm diff} = R_{\rm out}^2 - R_{\rm side}^2$ and the ratio $R_{\rm out}/R_{\rm side}$ are also investigated. The results show that the extracted radii $R_{\rm {side}}$ and $R_{\rm long}$ decrease with increasing transverse momentum and increase gradually with collision energy, while $R_{\rm {out}}$ shows little energy dependence. The Levy index $α$ exhibits only a mild dependence on $m_T$ and collision energy, whereas the correlation strength $λ$ shows a clear $m_T$ dependence and generally decreases with increasing collision energy. A comparison with EPOS3 results indicates general agreement within approximately 2$σ$, with the notable exception of $R_{\rm side}$, which is systematically smaller in EPOS4.