Kinetic Freeze-Out Conditions and Net Baryon Density in Au+Au Collisions at $\sqrt{s_{NN}} = 7.7$--$39$ GeV within a Collective Flow Fireball Model

TL;DR

This study uses a covariant fireball model to analyze how collective flow affects kinetic freeze-out conditions and net baryon density in Au+Au collisions across a range of energies, providing insights into the freeze-out parameters and baryon density evolution.

Contribution

It introduces a systematic analysis of longitudinal flow effects on freeze-out parameters using a covariant model, refining understanding of baryon density and temperature at different collision energies.

Findings

Longitudinal flow shifts temperature estimates upward, depending on flow velocity.

Temperatures at low flow velocities are consistent with lattice QCD crossover temperature.

Maximum net baryon density occurs at collision energies below 11.5 GeV.

Abstract

We investigate the effects of transverse and longitudinal collective flow on kinetic freeze-out conditions and net baryon density in 0--5\% central Au+Au collisions at $\sqrt{s_{NN}} = 7.7$--$39$ GeV within the RHIC Beam Energy Scan program. Using a covariant statistical fireball model, we fit the transverse momentum spectra of protons and positive pions from STAR data to simultaneously extract the kinetic freeze-out temperature $T$, baryon chemical potential $\mu_B$, and transverse flow velocity $v_T$, for three fixed longitudinal velocities $v_z = 0.0$, $0.2$, and $0.4$. Longitudinal flow induces a systematic upward shift in $T$, spanning $143$--$171$ MeV, $150$--$180$ MeV, and $175$--$209$ MeV for $v_z = 0$, $0.2$, and $0.4$, respectively, arising from a kinematic degeneracy between $v_z$ and $T$ in the Lorentz-invariant distribution function rather than from any hardening of the $p_T$ spectra. While temperatures extracted at $v_z = 0$ and $0.2$ are broadly consistent with the QCD crossover temperature $T_c \approx 155$--$160$ MeV expected from lattice QCD, the values obtained at $v_z = 0.4$ significantly exceed $T_c$, suggesting that the system would no longer be described by a hadron resonance gas at these conditions and indicating that large longitudinal velocities may be physically disfavored at these collision energies. The baryon chemical potential decreases monotonically from $\mu_B \sim 420$ MeV at $7.7$ GeV to $\sim 200$ MeV at $39$ GeV, independently of $v_z$. Reconstructing the freeze-out trajectory in the $(\rho_B, \varepsilon)$ plane, we identify a maximum in net baryon density at $\sqrt{s_{NN}} \lesssim 11.5$ GeV, with dynamical flow enhancing the inferred baryon compression by up to $\sim$20\% relative to the static limit. These results provide refined freeze-out benchmarks for future hydrodynamic modeling and for experiments at FAIR and low-energy RHIC runs.