Solvable model for spin polarizations with flow-momentum correspondence

We present an analytically solvable model based on the blast-wave picture of heavy-ion collisions with flow-momentum correspondence. It can describe the key features of spin polarization in heavy-ion collisions. With the analytical solution, we can clearly show that the spin polarization with respect to the reaction plane is driven by the directed flow, while the spin polarization along the beam direction is driven by the ellipticity in flow and in transverse emission area. There is a symmetry by interchanging $sinh\ensuremath{\rho}$ and $cosh\ensuremath{\rho}$ ($\ensuremath{\rho}$ is the transverse rapidity) between collective flow contributions to the spin polarization from the vorticity and from the shear stress tensor due to the flow-momentum correspondence. The solution can be improved systematically by perturbation method.