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

TL;DR

This work uses EPOS4-based 3D Lévy femtoscopy to probe the space-time structure of pion emission in heavy-ion collisions over BES energies ($7.7$–$200$ GeV). By extracting the Lévy index $α$, correlation strength $λ$, and the Bertsch-Pratt radii $R_{out}$, $R_{side}$, and $R_{long}$ from the 3D pair-distance distribution, it establishes how these observables depend on transverse mass $m_T$ and collision energy. The study finds that $R_{long}$ and $R_{side}$ grow with energy while $R_{out}$ is relatively energy-insensitive, and that $α$ varies mildly with $m_T$ and energy, with $λ$ generally decreasing with energy and increasing with $m_T$, including a few anomalies around certain energies. This work provides a theoretical baseline for interpreting experimental Lévy-femtoscopy data, informs possible EOS and critical-point signatures, and enables comparisons with EPOS3 and PHENIX measurements.

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.

Figures (10)

• Figure 1: Lévy index $\alpha$ from EPOS4 calculations as a function of transverse mass $m_T$ at different energies. The bands show the systematical uncertainties.
• Figure 2: Lévy index $\alpha$ from EPOS4 calculations as a function of collision energy $\sqrt{s_{NN}}$ in three bins of $k_T$. The bands show the systematical uncertainties.
• Figure 3: Lévy radii from EPOS4 calculations as a function of transverse momentum $m_T$ at $\sqrt{s_{NN}}=7.7-200~GeV$. The bands show the systematical uncertainties.
• Figure 4: Energy dependence of Lévy radii from EPOS4 calculations at $k_T = 0.375-0.425$ GeV/$c$. The bands show the systematical uncertainties.
• Figure 5: The radius difference $R_\mathrm{diff}^2$ from EPOS4 calculations as a function of collision energy $\sqrt{s_{NN}}$ in three $k_T$ bins. The bands show the systematical uncertainties.