Global $\mathrm{\Lambda }$ polarization in high energy collisions

With a Yang-Mills flux-tube initial state and a high-resolution (3+1)D particle-in-cell relativistic (PICR) hydrodynamics simulation, we calculate the $\mathrm{\Lambda }$ polarization for different energies. The origination of polarization in high energy collisions is discussed, and we find linear impact parameter dependence of the global $\mathrm{\Lambda }$ polarization. Furthermore, the global $\mathrm{\Lambda }$ polarization in our model decreases very quickly in the low energy domain, and the decline curve fits well the recent results of Beam Energy Scan (BES) program launched by the STAR Collaboration at the Relativistic Heavy Ion Collider (RHIC). The time evolution of polarization is also discussed.

Figure 1

The $y$ component (top) and the modulus (bottom) of the $\mathrm{\Lambda }$ polarization for momentum vectors in the transverse, $[p_x,p_y]$, plane at $p_z=0$, for the Au+Au reaction at $\sqrt{s_{NN}}=11.5$ GeV. The figure is in the frame of the $\mathrm{\Lambda }$. The impact parameter $b=0.7b_m=0.7\times 2R$, where $R$ is the radius of Au and $b_m=2R$ is the maximum value of $b$. The freeze-out time is $6.25=(2.5+4.75)$ fm/c, including 2.5 fm/c for initial state and 4.75 fm/c for hydroevolution.

Figure 2

The linear dependence of global polarization, $2{\langle {\mathrm{\Pi }}_{0y}\rangle }_p$, as a function of impact parameter ratio $b_0$ at 11.5, 27.0, and 62.4 GeV.

Figure 3

The global polarization, $2{\langle {\mathrm{\Pi }}_{0y}\rangle }_p$, in our PICR hydromodel (red circle) and STAR BES experiments (green triangle), at energies $\sqrt{s}$ of 11.5, 14.5, 19.6, 27.0, 39.0, 62.4, and 200 GeV. The experimental data were extracted from Ref. [24], with solid triangle for $\mathrm{\Lambda }$ and hollow triangle for $\overline{\mathrm{\Lambda }}$, dropping the error bars.

Figure 4

The time evolution of global polarization, $2{\langle {\mathrm{\Pi }}_{0y}\rangle }_p$, for energy $\sqrt{s}=11.5$, 27, and 62.4 GeV.