Polarization of $\mathrm{\Lambda }$ ($\overline{\mathrm{\Lambda }}$) Hyperons along the Beam Direction in $\mathrm{Au}+\mathrm{Au}$ Collisions at $\sqrt{s_{NN}}=200\mathrm{GeV}$

The $\mathrm{\Lambda }$ ($\overline{\mathrm{\Lambda }}$) hyperon polarization along the beam direction has been measured in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=200\mathrm{GeV}$, for the first time in heavy-ion collisions. The polarization dependence on the hyperons’ emission angle relative to the elliptic flow plane exhibits a second harmonic sine modulation, indicating a quadrupole pattern of the vorticity component along the beam direction, expected due to elliptic flow. The polarization is found to increase in more peripheral collisions, and shows no strong transverse momentum ($p_T$) dependence at $p_T$ greater than $1\mathrm{GeV}/c$. The magnitude of the signal is about 5 times smaller than those predicted by hydrodynamic and multiphase transport models; the observed phase of the emission angle dependence is also opposite to these model predictions. In contrast, the kinematic vorticity calculations in the blast-wave model tuned to reproduce particle spectra, elliptic flow, and the azimuthal dependence of the Gaussian source radii measured with the Hanbury Brown–Twiss intensity interferometry technique reproduce well the modulation phase measured in the data and capture the centrality and transverse momentum dependence of the polarization signal.

Figure 1

A sketch illustrating the system created in a noncentral heavy-ion collision viewed in the transverse plane ($x\text{−}y$), showing stronger in-plane expansion (solid arrows) and expected vorticities (open arrows). Here, the colliding beams are oriented along the $z$ axis and the $x\text{−}z$ plane defines the reaction plane. See text for explanations of ${\varphi }_s$ and ${\varphi }_b$.

Figure 2

$⟨\cos {\theta }_p^{*}⟩$ of $\mathrm{\Lambda }$ and $\overline{\mathrm{\Lambda }}$ hyperons as a function of azimuthal angle $\varphi$ relative to the second-order event plane ${\mathrm{\Psi }}_2$ for 20%–60% centrality bin in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=200\mathrm{GeV}$. Open boxes show the systematic uncertainties and $⟨{⟩}^{\mathrm{sub}}$ denotes the subtraction of the acceptance effect (see text). Solid lines show the fit with the sine function shown inside the figure. Note that the data are not corrected for the event plane resolution.

Figure 3

The second Fourier sine coefficient of the polarization of $\mathrm{\Lambda }$ and $\overline{\mathrm{\Lambda }}$ along the beam direction as a function of the collision centrality in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=200\mathrm{GeV}$. Open boxes show the systematic uncertainties. Dotted line shows the AMPT calculation [32] scaled by 0.2 (no $p_T$ selection). Solid and dot-dashed lines with the bands show the blast-wave (BW) model calculation for $p_T=1\mathrm{GeV}/c$ with $\mathrm{\Lambda }$ mass (see text for details).

Figure 4

The second Fourier sine coefficient of the longitudinal polarization of $\mathrm{\Lambda }$ and $\overline{\mathrm{\Lambda }}$ hyperons as a function of $p_T$ for 20%–60% centrality bin in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=200\mathrm{GeV}$. Open boxes show the systematic uncertainties. Magenta dashed line shows the hydrodynamic model calculation [18] scaled by 0.2. Solid and dot-dashed lines with the bands show the blast-wave model calculations with $\mathrm{\Lambda }$ mass.