Dynamically integrated transport approach for heavy-ion collisions at high baryon density

We develop a new dynamical model for high-energy heavy-ion collisions in the beam energy region of the highest net-baryon densities on the basis of nonequilibrium microscopic transport model jam and macroscopic ($3+1$)-dimensional hydrodynamics by utilizing a dynamical initialization method. In this model, dynamical fluidization of a system is controlled by the source terms of the hydrodynamic fields. In addition, time-dependent core-corona separation of hot regions is implemented. We show that our new model describes multiplicities and mean transverse mass in heavy-ion collisions within a beam-energy region of $3<\sqrt{s_{NN}}<30$ GeV. Good agreement of the beam-energy dependence of the $K^{+}/{\pi }^{+}$ ratio is obtained, which is explained by the fact that a part of the system is not thermalized in our core-corona approach.

Figure 1

Time evolution of the energy density at the coordinate origin $(x,y,z)=(0,0,0)$ from jam hybrid simulations with $e_{\text{f}}=e_{\text{p}}=0.5\mathrm{GeV}/{\mathrm{fm}}^3$ in central $\text{Pb}+\text{Pb}$ collisions at $\sqrt{s_{NN}}=6.4$ GeV ($E_{\text{lab}}=20A$ GeV). The upper panel shows the results from calculations by the fixed switching time at $t_{\text{sw}}=4\mathrm{fm}/c$. The result from a dynamical initialization is shown in the lower panel. The circles show the contribution from particles, and the squares show the fluid contribution to the energy density.

Figure 2

Time evolution of the fractions of the fluid energy for $e_{\text{f}}=0.5\mathrm{GeV}/{\mathrm{fm}}^3$ (upper panel) and $e_{\text{f}}=1.0\mathrm{GeV}/{\mathrm{fm}}^3$ (lower panel) at the central region $\left|z\right|<1.0$ fm from jam hybrid simulations in central $\text{Au}+\text{Au}$ at $\sqrt{s_{NN}}=2.7,3.3$, and 4.9 GeV, and $\text{Pb}+\text{Pb}$ collisions at $\sqrt{s_{NN}}=12.4$ and 17.3 GeV.

Figure 3

Rapidity distributions of protons, negatively charged pions, negatively and positively charged kaons, and $\mathrm{\Lambda }\mathrm{s}$ in the central $\text{Pb}+\text{Pb}$ collisions at $\sqrt{s_{NN}}=6.4$ GeV. The results from jam cascade (dashed lines) and jam + hydro calculations with $e_{\text{f}}=0.5$ (dotted lines) and $1.0\mathrm{GeV}/{\mathrm{fm}}^3$ (solid lines) are compared with the experimental data [38, 68, 69].

Figure 4

Same as Fig. 3, but the results from jam + hydro simulations in which leading particles are also converted into fluid after their formation times (dashed lines), the results from the calculations without formation times but leading particles are not converted into fluid (solid lines), and the results from the calculations without formation times for all particles including leading particles.

Figure 5

Transverse mass distributions of protons, negative pions, and positive and negative kaons in central $\text{Pb}+\text{Pb}$ collisions at $\sqrt{s_{NN}}=6.4$ GeV. The results from jam cascade (dashed lines) and jam + hydro calculations with $e_{\text{f}}=0.5$ (solid lines) and $1.0\mathrm{GeV}/{\mathrm{fm}}^3$ (dotted lines) are compared with experimental data [38, 70].

Figure 6

Beam-energy dependence of particle multiplicities at midrapidity in central $\text{Au}+\text{Au}$ and $\text{Pb}+\text{Pb}$ collisions. The experimental data are taken from Refs. [71, 72, 73, 74, 75]. jam + hydro results for (anti-)protons with weak-decay contributions (dashed-dotted lines) are compared with the STAR data which contain the weak-decay feed-down contributions to (anti)-proton yield.

Figure 7

Beam-energy dependence of mean transverse mass for pions, kaons, protons, antiprotons, $\mathrm{\Lambda }\mathrm{s}$, and anti-$\mathrm{\Lambda }\mathrm{s}$ at midrapidity in central $\text{Au}+\text{Au}$ and $\text{Pb}+\text{Pb}$ collisions. The experimental data are taken from Refs. [1, 68, 70, 79].

Figure 8

Beam-energy dependence of $K/\pi$ ratios at midrapidity in central $\text{Au}+\text{Au}$ and $\text{Pb}+\text{Pb}$ collisions. The experimental data are taken from Refs. [1, 37, 38].

Figure 9

Beam-energy dependence of $(\mathrm{\Lambda }+{\mathrm{\Sigma }}^0)/{\pi }^{-}$ ratio at midrapidity in central $\text{Au}+\text{Au}$ and $\text{Pb}+\text{Pb}$ collisions. The experimental data are taken from Refs. [82, 83].