Pion emission source shape in UrQMD Au+Au collisions at STAR energies

Abstract

Femtoscopic measurements of two-pion Bose--Einstein correlations have established that particle-emitting sources in heavy-ion collisions are well described by Lévy $\alpha$-stable distributions, motivating systematic studies across a wide range of collision energies. In this work, we present a three-dimensional femtoscopic analysis of pion pairs in Au+Au collisions simulated with the UrQMD model for collision energies $\sqrt{s_{NN}}=3$--$27\mathrm{GeV}$, taking the RHIC BES-II range of collider and fixed target experiment energies for reference. Using Lévy-type source parameterisations, we extract the pair multiplicity parameter ${\lambda }^{\ast }$ (related to the correlation strength $\lambda$), Lévy index $\alpha$, and three-dimensional radii $R_{\mathrm{out}}$, $R_{\mathrm{side}}$, and $R_{\mathrm{long}}$. We investigate their dependence on the transverse mass ($m_T$) and collision energy, along with derived quantities such as the radius difference $R_{\mathrm{diff}}^2=R_{\mathrm{out}}^2-R_{\mathrm{side}}^2$ and the ratio $R_{\mathrm{out}}/R_{\mathrm{side}}$. We find that $R_{\mathrm{out},\mathrm{side},\mathrm{long}}$ all decrease with increasing $m_T$ and increase with collision energy, consistent with collective expansion, $R_{\mathrm{long}}$ showing the strongest and $R_{\mathrm{side}}$ the weakest energy dependence. The Lévy index $\alpha$ decreases with collision energy, with a larger $m_T$-dependence towards higher energies. The ${\lambda }^{\ast }$ parameter is consistent with a constant close to unity in the absence of pions from long-lived resonances. These results provide a baseline for future comparisons with experimental measurements from the STAR Collaboration, contributing to constraints on the QCD phase diagram.

Comments: 11 pages, 7 figures, data file included