Azimuthal angle dependence of the longitudinal spin polarization in relativistic heavy ion collisions

The longitudinal quark spin polarization along the beam direction in noncentral relativistic heavy ion collisions is studied in the chiral kinetic approach. Its azimuthal angle dependence in the transverse plane of the collision is found to have a quadrupole structure as in studies from hydrodynamic and transport models based on the relativistic spin-vorticity coupling in a thermodynamically equilibrated hadronic matter at kinetic freeze-out. The direction of the quark longitudinal spin polarization is, however, opposite to that from these models, and this is due to the axial charge current induced by the transverse component of the vorticity field in the chiral kinetic approach. Our finding is consistent with the azimuthal angle dependence of the longitudinal spin polarization of $\mathrm{\Lambda }$ hyperons, which is mainly determined by that of the strange quark, recently measured in the experiments by the STAR Collaboration at the BNL Relativistic Heavy Ion Collider.

Figure 1

Distributions of the in-plane $x$ component ${\omega }_x$ of the vorticity field (arrows) [20] and the induced axial charge distribution (plus and minus signs) in the transverse plane of a heavy ion collision.

Figure 2

Time evolution of different components of average vorticity field in midrapidity ($\left|y\right|<1$) for selected regions of the transverse plane.

Figure 3

Time evolution of average longitudinal spin polarization of midrapidity quarks with momenta satisfying $p_x{p}_y>0$.

Figure 4

Average longitudinal spin polarization of quarks as a function of azimuthal angle ${\varphi }_p$ of the quark momentum in the transverse plane for different rapidity ranges.

Figure 5

Same as Fig. 4 but for strange quarks.