Spectra and elliptic flow of light hadrons in an expanding fire-cylinder model for the RHIC Beam Energy Scan

TL;DR

This work introduces an expanding elliptic fire-cylinder, blast-wave–like model to describe $p_T$ spectra and elliptic flow $v_2(p_T)$ of light hadrons in peripheral Au+Au collisions across the RHIC BES energy range. The expansion history is fixed by fitting midrapidity $\pi^{\pm}$ spectra, then applied to $K^{\pm}$ and $p(\bar p)$ with particle-specific chemical potentials to match yields, providing a unified description of soft hadron production. The model captures the qualitative trends of $v_2(p_T)$ and reveals how anisotropic expansion parameters $\Delta v$ and $B$ drive flow, with stronger flow at higher $\sqrt{s_{NN}}$ and a natural evolution of the source eccentricity and volume. While ignoring resonance decays and baryon stopping, the approach offers a compact, coherent baseline for low-energy heavy-ion phenomenology and sets the stage for extensions to centrality dependence, higher-order flow, and penetrating probes.

Abstract

We investigate the transverse momentum spectra ($p_T$) and elliptic flow ($v_2$) of $π^{\pm}$, $K^{\pm}$, $p$, and $\bar{p}$ produced in peripheral Au+Au collisions at $\sqrt{s_{\rm NN}} = 7.7$, 11.5, 19.6, 27, and 39 GeV in the Beam Energy Scan (BES) Program at the Relativistic Heavy Ion Collider (RHIC). The analysis is carried out within an expanding elliptic fire-cylinder model that incorporates longitudinal expansion and anisotropic transverse flow. Particle production at kinetic freeze-out is obtained using a local equilibrium distribution function with a blast-wave-like fluid velocity profile derived from the expansion dynamics of the elliptic fire-cylinder. The model parameters governing the collective expansion are first constrained by fitting the midrapidity $p_T$ spectra of $π^{\pm}$ and are then applied, without further adjustment, to $K^{\pm}$, $p$, and $\bar{p}$. The model provides a consistent description of the $p_T$ spectra and reproduces the qualitative behavior of the elliptic flow for all considered particle species.

Figures (12)

• Figure 1: (Color online) Calculated $p_T$ spectra of pions obtained using the fitted expansion parameters of Table \ref{['tab:model_params']}.
• Figure 2: (Color online) Time evolution of spatial eccentricity $\epsilon(t)$ of the expanding elliptic fire-cylinder for different collision energies $\sqrt{s_{\rm NN}}$. End points denote the freeze-out times for different $\sqrt{s_{\rm NN}}$.
• Figure 3: (Color online) Time evolution of the volume $V(t)$ of the expanding elliptic fire-cylinder for different collision energies $\sqrt{s_{\rm NN}}$.
• Figure 4: (Color Online) Rapidity distribution of $\pi^{+}$ (upper panel) and $\pi^{-}$ (lower panel) for mid-central ($40$--$50\%$) collisions at different beam energies $\sqrt{s_{\rm NN}}$ compared with the experimental data STAR:2017sal at mid-rapidity.
• Figure 5: (Color online) Calculated $p_T$ spectra of protons ($p$) (top-left), anti-protons ($\bar{p}$) (top-right), positively charged kaons ($K^{+}$) (bottom-left), and negatively charged kaons ($K^{-}$) (bottom-right) at mid-rapidity compared with the data from STAR:2017sal.