Pushing the hybrid approach to low beam energies with dynamic initial conditions from hadronic transport

TL;DR

The paper addresses the challenge of modeling low-energy heavy-ion collisions where boost invariance fails and equilibration is spatially and temporally inhomogeneous. It introduces dynamic fluidization (DynFlu), a core-corona separation based on a local energy-density threshold and a string-fluidization time, coupling SMASH transport to 3+1D viscous hydrodynamics (vHLLE) with a fixed particlization threshold (epsilon_sw). The approach extends the hybrid framework to the 3–9.1 GeV regime, achieving good agreement with bulk observables and offering predictions for forward rapidities and flow, while highlighting areas for improvement such as kaon yields and electromagnetic probes. This work provides a path to study the QCD phase diagram, including potential phase-transition effects, by enabling realistic, event-by-event hydrodynamic evolution at low beam energies and informing upcoming STAR-BES and CBM measurements.

Abstract

While hybrid approaches of relativistic hydrodynamics+transport have been well established for the dynamical description of heavy-ion collisions at high beam energies, moving to lower beam energies is challenging. In this work, we propose dynamic initial conditions for the viscous hydrodynamic evolution in heavy-ion collisions at low to intermediate beam energies. They are comprised of core hadrons based on the local energy density during the pre-equilibrium hadronic evolution. The SMASH-vHLLE hybrid approach is then applied to lower beam energies, achieving good agreement with measured bulk observables between $\sqrt{s_\mathrm{NN}} = 3$ and $9.1\ \mathrm{GeV}$, thus providing guidance for measurements in STAR-BES and CBM at FAIR.

Figures (14)

• Figure 1: Energy density profile of a head-on Au+Au collision in the transverse plane at $z=0$ (upper) and $t=1.5\ \mathrm{fm}$ at $\sqrt{s_{\rm NN}}=3.5\ \mathrm{GeV}$ (lower) and $t=1.0\ \mathrm{fm}$ at $\sqrt{s_{\rm NN}}=7.7\ \mathrm{GeV}$. The white lines denote $\varepsilon=0.3,0.5,$ and $0.8\ \mathrm{GeV}/\mathrm{fm}^3$.
• Figure 2: Evolution of (left) the mean energy density $\left\langle\varepsilon\right\rangle$, (middle) its event-by-event fluctuation $\sigma_\varepsilon$, and (right) the ratio $\sigma_\varepsilon/\left\langle\varepsilon\right\rangle$ in different spatial points (with $y=0$) for a head-on Au+Au collision at $\sqrt{s_{\rm NN}}=3.5\ \mathrm{GeV}$.
• Figure 3: Spacetime distribution of energy deposition within our core-corona separation for head-on Au+Au collisions at different beam energies, using $\varepsilon_\mathrm{th}=0.5\ \mathrm{GeV}/\mathrm{fm}^3$ and $t_f=0.25\ \mathrm{fm}$. The black hyperbolas show the constant hypersurface of constant $\tau$ defined by the nuclear passing time $\tau_0$\ref{['eq:constant_tau']}.
• Figure 4: Evolution of the total energy present in the fluid during the hydrodynamic stage, initialized with the dynamic (full lines) vs. iso-$\tau$ (dashed lines) initial conditions.
• Figure 5: Trajectories of the fluid in the phase diagram. Each dot is an average value $\left\langle\mu_B\right\rangle_\varepsilon$ and $\left\langle T\right\rangle_\varepsilon$, and the ellipsis around each point represents their 1$\sigma$ spread (see text). The dashed black curve shows the particlization at $\varepsilon_\mathrm{sw}=0.334\ \mathrm{GeV}/\mathrm{fm}^3$.