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

The azimuthal angle dependence of quark spin polarization in the longitudinal beam direction of non-central relativistic heavy ion collisions is studied in the chiral kinetic approach. Contrary to the prediction from models based on the assumption of thermal equilibrium of spin degrees of freedom that the quark spin polarization always points along the direction of local vorticity field, we find the two can have opposite directions due to the effect from the transversal component of vorticity field, which can lead to a redistribution of axial charges in the produced matter. Our finding is consistent with the azimuthal angle dependence of the longitudinal spin polarization of $Lambda$ hyperons, which is mainly determined by that of the strange quark, recently measured in the experiments by the STAR Collaboration at the Relativistic Heavy Ion Collider (RHIC).