Probing early-time longitudinal dynamics with the $\Lambda$’s polarization in relativsitic heavy-ion collisions

We systematically study the global $\Lambda$ polarization sensitivity to collision systems’ initial longitudinal flow velocity in hydrodynamic simulations. By explicitly imposing energy-momentum conservation when mapping the initial collision geometry to macroscopic hydrodynamic fields, we study the evolution of systems’ orbital angular momentum and fluid vorticity. The spin polarization of $\Lambda$ is compared with the STAR measurements in the Au+Au collisions from 7.7 GeV to 200 GeV. We further extend our model to make predictions for Pb+Pb collisions at 5020 GeV and Au+Au collisions at 3 GeV in the STAR fix target experiments at RHIC.