Lévy sources in UrQMD in Ar+Sc collisions at SPS energies

TL;DR

The paper investigates three-dimensional two-pion source distributions in $^{40}$Ar+$^{45}$Sc collisions at SPS energies using the UrQMD transport model, extracting Lévy-stable parameters ($\alpha$, $R_{\text{out}}$, $R_{\text{side}}$, $R_{\text{long}}$, $\lambda^*$) by fitting projected pair-source distributions with Lévy forms. It demonstrates that Lévy distributions provide a good description of the simulated pair-distance data and maps how $\alpha$ increases with transverse mass $m_T$ while decreasing with collision energy, whereas the radii shrink with $m_T$ and grow with energy; $\lambda^*$ increases modestly with $m_T$ but is biased high due to missing weak decays in the model. The work identifies a systematic bias from absent weak decays, quantifies it as a roughly 7–8% effect on $\lambda^*$, and provides a baseline for interpreting experimental femtoscopy and for validating transport models across SPS energies. Overall, the study contributes to understanding non-Gaussian emission sources and informs future analyses of heavy-ion collisions through Lévy-source characterizations, including potential links to Lévy walks and diffusion mechanisms in the emission process.

Abstract

Over the past few decades, progress in femtoscopy has been driven by the interplay between experimental measurements and theoretical calculations. Measurements provide data for the theory to understand it, while theoretical predictions guide new measurements. In the recent decade, several experiments have confirmed that the two-particle pion emitting source is well described by Lévy alpha-stable distributions. To enable theoretical interpretation, phenomenological simulations have been done at RHIC and LHC energies, using various available heavy-ion collision models. In this paper, we investigate three-dimensional two-pion pair source distributions from $^{40}$Ar+$^{45}$Sc central collisions at SPS energies, generated with the Ultra-Relativistic Quantum Molecular Dynamics Monte-Carlo event generator. We fit the pair source with Lévy-stable distributions, and discuss the extracted Lévy parameters describing the spatial scale, shape and strength of the source.

Figures (5)

• Figure 1: Example fit (red line) to projected $D(\rho)$ distributions (blue points) in Ar+Sc 0-10% centrality at 40A GeV/$c$ in $K_\text{T}$ range [0.15-0.18] GeV/$c$ with 2500 events merged. The fit is marked with a solid line, while the dashed line is an extrapolation.
• Figure 2: The Lévy index parameter $\alpha$, for 0--10% central Ar+Sc. For all transverse mass $m_\text{T}$ a), for selected transverse mass $m_\text{T}$ intervals b), and the average of all transverse mass $m_\text{T}$ intervals at the given energies c). The given colored band shows systematic uncertainty.
• Figure 3: The intercept parameter $\lambda^*$, for 0--10% central Ar+Sc at all beam momenta, as a function of transverse mass $m_\text{T}$. The given colored band shows systematic uncertainty.
• Figure 4: The Lévy-scale parameters $R_\text{out, side, long}$, for 0--10% central Ar+Sc at all beam momenta, as a function of transverse mass $m_\text{T}$. The colored bands show the systematic uncertainty.
• Figure 5: The averaged Lévy-scale parameter $\bar{R}$, for 0--10% central Ar+Sc. For all transverse mass $m_\text{T}$ as a function of $m_\text{T}$ a) and for selected transverse mass $m_\text{T}$ intervals as a function of beam momentum b). The given colored band shows systematic uncertainty.