From chiral kinetic theory to relativistic viscous spin hydrodynamics

In this paper, we start with chiral kinetic theory and construct the spin hydrodynamic framework for a chiral spinor system. Using the 14-moment expansion formalism, we obtain the equations of motion of second-order dissipative relativistic fluid dynamics with nontrivial spin-polarization density. In a chiral spinor system, the spin-alignment effect could be treated in the same framework as the chiral vortical effect (CVE). However, the quantum corrections due to fluid vorticity induce not only CVE terms in the vector/axial charge currents, but also corrections to the stress tensor. In this framework, viscous corrections to the hadron spin polarization are self-consistently obtained, which will be important for precise prediction of the polarization rate for the observed hadrons, e.g., $\mathrm{\Lambda }$ hyperon.