Net-baryon diffusion in fluid-dynamic simulations of relativistic heavy-ion collisions

A hybrid (hydrodynamics + hadronic transport) theoretical framework is assembled to model the bulk dynamics of relativistic heavy-ion collisions at energies accessible in the beam energy scan program at the Relativistic Heavy-Ion Collider and the NA61/SHINE experiment at CERN. The system's energy-momentum tensor and net-baryon current are evolved according to relativistic hydrodynamics with finite shear viscosity and nonzero net-baryon diffusion. Our hydrodynamic description is matched to a hadronic transport model in the dilute region. With this fully integrated theoretical framework, we present a pilot study of the hadronic chemistry, particle spectra, and anisotropic flow. Phenomenological effects of a nonzero net-baryon current and its diffusion on hadronic observables are presented for the first time. The importance of the hadronic transport phase is also investigated.

Figure 1

Example of the envelope functions for (a) entropy density and (b) net-baryon density $f_{\pm }^s\left({\eta }_s\right)$ and $f_{\pm }^{n_B}\left({\eta }_s\right)$ in Au+Au collisions at $\sqrt{s_{\mathrm{NN}}}=19.6$ GeV.

Figure 2

The temperature and net-baryon chemical potential dependence of (a) the net-baryon diffusion constant and (b) specific shear viscosity for $C_B=0.4$ and $C_{\eta }=0.08$, respectively.

Figure 3

(a) The square of the speed of sound as a function of the local energy density along constant $s/n_B$ lines. (b) Temperature as a function of net-baryon chemical potential along constant $s/n_B$ lines. The collision energies correspond to these $s/n_B$ lines (from top down in the legend) are $\sqrt{s_{\mathrm{NN}}}=200,62.4,19.6$, and 14.5 GeV according to Ref. [35].

Figure 4

Constant energy density freeze-out lines compared with the extracted chemical freeze-out points from the STAR collaborations [4].

Figure 5

Time evolution of the ${\mu }_B/T$ along (a) longitudinal direction for points at $x=0$ and $y=0$ and (b) transverse plane along $y=0$ and ${\eta }_s=0$.

Figure 6

(a) The pseudorapidity and rapidity distributions of the charged hadron, identified ${\pi }^{+}$, and $K^{+}$ compared to the PHOBOS and STAR measurements in 0–5 % Au+Au collisions at 19.6 GeV [4, 28]. (b) The net-proton rapidity distribution with different choices of the net-baryon diffusion constant compared with the STAR measurements.

Figure 7

(a) The fit of the net-proton rapidity distribution with different choices of the net-baryon diffusion constant in the simulations. (b) The single particle spectra of ${\pi }^{+}$ and $K^{+}$ with different choices of the net-baryon diffusion constant. (c) The single-particle spectra of proton and antiproton with different choices of the net-baryon diffusion constant.

Figure 8

The $p_T$-differential elliptic flow coefficients of identified (a) ${\pi }^{+}$, (b) $p$, and (c) $\overline{p}$ with different net-baryon diffusion constants in the hydrodynamic simulations for 20–30 % Au+Au collisions at 19.6 GeV. The shaded bands indicate statistical errors.

Figure 9

The effects of the out-of-equilibrium corrections $\delta f$ from shear viscosity and net-baryon number diffusion on the net-proton rapidity distribution.

Figure 10

The correction of shear and net-baryon diffusion $\delta f$ to the transverse momentum spectra of (a) ${\pi }^{+},K^{+}$, and (b) $p$, and $\overline{p}$ at the midrapidity in the hybrid simulations.

Figure 11

The correction of shear and net-baryon diffusion $\delta f$ to the $p_T$ differential $v_2$ of (a) ${\pi }^{+}$, (b) $p$, and (c) $\overline{p}$ in hybrid simulations. The shaded bands indicate statistical errors.

Figure 12

The effects of hadronic rescatterings on (a) charged hadron and (b) net-proton rapidity distribution.

Figure 13

The effects of hadronic transport on the transverse momentum spectra of final (a) ${\pi }^{+},K^{+}$, (b) $p$, and $\overline{p}$.

Figure 14

The effects of hadronic transport on the differential $v_2$ of final (a) ${\pi }^{+}$, (b) $p$, and (c) $\overline{p}$. The shaded bands indicate statistical errors.

Figure 15

Cross check the pseudorapidity distribution of thermally emitted (a) ${\pi }^{+}$, and (b) $p$, and $\overline{p}$ between the numerical results from Cooper-Frye formula (lines) and the statistical results from particle sampler iSS (markers).

Figure 16

Cross check the $p_T$ spectra of thermally emitted (a) ${\pi }^{+}$, and (b) $p$, and $\overline{p}$ between the numerical results from Cooper-Frye formula (lines) and the statistical results from particle sampler iSS (markers).

Figure 17

Cross check the $p_T$ differential $v_2$ of thermally emitted (a) ${\pi }^{+}$, and (b) $p$, and $\overline{p}$ between the numerical results from Cooper-Frye formula (lines) and the statistical results from particle sampler iSS (markers).

Figure 18

The evolution of (a) net-baryon density $n_B$ and (b) flow velocity $u^x$ compared with analytic Gubser solution (light solid lines in the background).

Figure 19

The evolution of (a) local energy density $e$ and (b) net-baryon density $n_B$ compared with (1+1)D numerical solutions (markers).

Figure 20

The (pseudo)rapidity distribution of (a) charged hadrons and (b) net protons from the two hadronic cascade simulations for 0–5 % centrality Au+Au collisions at 19.6 GeV.

Figure 21

The comparison of $p_T$ spectra of final (a) ${\pi }^{+}$ and $K^{+}$ and (b) $p$ and $\overline{p}$ from the two hadronic cascade simulations.

Figure 22

The $p_T$ differential $v_2$ of final (a) ${\pi }^{+}$ and $K^{+}$ and (b) $p$ from the two hadronic cascade simulations. The shaded bands indicate statistical errors.