Global $\mathrm{\Lambda }$ polarization in heavy-ion collisions from a transport model

The polarizations of $\mathrm{\Lambda }$ and $\overline{\mathrm{\Lambda }}$ hyperons are important quantities in extracting the fluid vorticity of the strongly coupled quark gluon plasma and the magnitude of the magnetic field created in off-central heavy-ion collisions, through the spin-vorticity and spin-magnetic coupling. We computed the energy dependence of the global $\mathrm{\Lambda }$ polarization in off-central Au+Au collisions in the energy range $\sqrt{s_{NN}}=7.7–200$ GeV using a multiphase transport model. The observed polarizations with two different impact parameters agree quantitatively with recent STAR measurements. The energy dependence of the global $\mathrm{\Lambda }$ polarization is decomposed as energy dependence of the $\mathrm{\Lambda }$ distribution at hadronization and the space-time distribution of the fluid-vorticity field. The visualization of both the $\mathrm{\Lambda }$ distribution and the fluid-vorticity field show a smaller tilt at higher collisional energies, which indicates that the smaller global polarization at higher collisional energies is caused by a smaller angular momentum deposition at midrapidity.

Figure 1

Schematic picture of an off-central collision.

Figure 2

The global $\mathrm{\Lambda }$ polarization at two impact parameters $b=7$ fm (the blue lower line) and 9 fm (the cyan upper line).

Figure 3

The global $\mathrm{\Lambda }$ polarization at energies from 7.7 GeV to 200 GeV. The blue solid line represents the global polarization of primary $\mathrm{\Lambda }\mathrm{s}$ and the black dashed line shows global polarization of primary plus feed-down $\mathrm{\Lambda }\mathrm{s}$. The unfilled squares and circles represent the global $\mathrm{\Lambda }$ and $\overline{\mathrm{\Lambda }}$ polarization measurements at STAR [25, 34].

Figure 4

The distribution of the $\mathrm{\Lambda }$'s production position integrated over $t$ and $y$ as a function of $x$ and $\eta$ at $\sqrt{s_{NN}}=7.7$ GeV (upper panel) and 200 GeV (lower panel). The midrapidity region $\left|\eta \right|<1$ is between the black dashed lines.

Figure 5

The thermal vorticity ${\varpi }_{zx}$ on the reaction plane ($y=0$) at $t=5\text{fm}/c$ at $\sqrt{s_{NN}}=7.7$ GeV (upper panel) and 200 GeV (lower panel). The black dashed lines represent the contour where ${\varpi }_{zx}=0$.

Figure 6

The distribution of the number of $\mathrm{\Lambda }$ hyperons $dN/d{\varpi }_{zx}$.