Theoretical modeling of fluid vorticity and spin polarization

Vorticity is a ubiquitous feature of collective properties of strongly-coupled fluid. Non-central heavy-ion collisions carry angular momenta of the order of 1,000 $hbar$ and can lead to a strong vortical structure inside the resulting Quark-Gluon Plasma (QGP) liquid. A local fluid rotation can induce a preferential orientation on the spins of the emitted particles through spin-orbit coupling. This talk summarizes the recent theoretical studies of $Lambda$ hyperon’s polarization observables with (3+1)D relativistic hydrodynamics in heavy-ion collisions. The effects of initial hot spot size and QGP’s specific shear viscosity on the polarization observables are quantified. We also examine the effects of the two formulations of the thermal shear tensor on the polarization observables using the same hydrodynamic background. With event-by-event simulations, we highlight new correlations among the Fourier coefficients of $Lambda$’s longitudinal polarization P^z and charged hadron anisotropic flow coefficients, which can further test the mapping from fluid velocity gradients to hyperon polarization.