Spin polarization of an expanding and rotating system

We study the longitudinal spin polarization of a relativistic fluid of massive spin-$1/2$ particles undergoing a boost-invariant expansion in the longitudinal direction and rotating in the transverse plane. We express the polarization vector in terms of spin moments and derive closed equations of motion for the latter using spin kinetic theory with a nonlocal relaxation time approximation. These equations of motion are valid at any time of the evolution, from the free-streaming regime to the hydrodynamic regime. At late time, the polarization features contributions from gradients of the fluid velocity and of the temperature that emerge from the nonlocal part of the collision term. Our results can be used to explore polarization phenomena in the context of heavy-ion collisions.