Dynamical initial-state model for relativistic heavy-ion collisions

We present a fully three-dimensional model providing initial conditions for energy and net-baryon density distributions in heavy-ion collisions at arbitrary collision energy. The model includes the dynamical deceleration of participating nucleons or valence quarks, depending on the implementation. The duration of the deceleration continues until the string spanned between colliding participants is assumed to thermalize, which is either after a fixed proper time, or a fluctuating time depending on sampled final rapidities. Energy is deposited in space time along the string, which in general will span a range of space-time rapidities and proper times. We study various observables obtained directly from the initial-state model, including net-baryon rapidity distributions, two-particle rapidity correlations, as well as the rapidity decorrelation of the transverse geometry. Their dependence on the model implementation and parameter values is investigated. We also present the implementation of the model with 3+1-dimensional hydrodynamics, which involves the addition of source terms that deposit energy and net-baryon densities produced by the initial-state model at proper times greater than the initial time for the hydrodynamic simulation.

Figure 1

Nucleon positions as a function of one transverse ($x$) and the longitudinal direction ($z$) for two different collision energies.

Figure 2

The nuclear overlapping time of 0%–5% central d+Au and Au+Au collisions as a function of the collision energy at the RHIC BES program.

Figure 3

The trajectories of the endpoints of the decelerating strings with different initial rapidities in $t-z$ (a) and $\tau -{\eta }_s$ (b) coordinates.

Figure 4

The space-time distribution of the strings at their thermalization in a Au+Au collision at 200 GeV and 19.6 GeV in $t-z$ and $\tau -{\eta }_s$ coordinates. The black dots indicate the space-time position of the net-baryon charges.

Figure 5

Same as for Fig. 4 but for a d+Au collision at 200 GeV and 19.6 GeV.

Figure 6

The average string deceleration time $\mathrm{\Delta }\tau$ as a function of the initial string rapidity in the LEXUS model. The black points indicate the RHIC BES collision energies, 5, 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4, and 200 GeV.

Figure 7

The space-time rapidity distributions of charged hadrons and net-baryon numbers from the four initial conditions for 0%–5% Au+Au collisions at 200 GeV (a) and 19.6 GeV (b).

Figure 8

Contour plots for the correlation of the net-baryon rapidity in momentum space to its space-time rapidity ${\eta }_s$ from the valence quark + rapidity loss fluctuation model for 0%–5% Au+Au collisions at 200 GeV (a) and 19.6 GeV (b).

Figure 9

The rapidity distribution of net protons from the four different initial-state models coupled with hydrodynamics + hadronic cascade simulations in central Pb+Pb collisions at the top SPS energy [38].

Figure 10

The rapidity distributions of charged hadrons (a) and net protons (b) at four different collision energies from our hybrid simulations with the model using valence quarks + rapidity loss fluctuations.

Figure 11

The longitudinal fluctuation coefficients $\left\{a_{1,1}\right\}$ for initial energy (a) and net-baryon number (b) density profiles as functions of collision energy in 0%–5% Au+Au collisions. The rapidity window is chosen to be $\left|y\right|<0.72$ to be consistent with the current STAR measurements.

Figure 12

The participant plane decorrelation coefficients $r_{2,3}({\eta }_a,{\eta }_b=2.0)$ in 0%–5% Au+Au collisions at 200 GeV for four different models.

Figure 13

The participant plane decorrelation coefficients $r_{2,3}({\eta }_a,{\eta }_b=2.0)$ in 0%–5% Au+Au collisions at different collision energies.

Figure 14

The ratios of proton fluctuation moments, $C_2/C_1={\sigma }^2/M, C_3/C_2=S\sigma , C_4/C_2=\kappa {\sigma }^2$, as functions of the collision energy from the valence quark + rapidity loss fluctuation model. Their dependence on the rapidity cut window are shown.

Figure 15

Same as Fig. 14 but for comparison among different models at the same rapidity window, $\left|y\right|<0.5$.