Directed flow and global polarization in Au+Au collisions across energies covered by the beam energy scan at RHIC

We study the directed flow of identified particles in Au+Au collisions at $\sqrt{{s}_{NN}}=7.7$ to 62.4 GeV. The Glauber model is extended to include both a tilted deformation of the QGP fireball with respect to the longitudinal direction and a non-zero longitudinal flow velocity gradient in the initial state. By combining this improved initial condition with a (3+1)-dimensional viscous hydrodynamic model calculation, we obtain a satisfactory description of the transverse momentum spectra and the rapidity dependent directed flow coefficient of different hadron species. Our calculation indicates the sensitivity of the hadron directed flow, especially its splitting between protons and antiprotons, to both the initial geometry and the initial longitudinal flow velocity. Therefore, the combination of directed flow of different hadrons can provide a tight constraint on the initial condition of nuclear matter created in heavy-ion collisions. The initial condition extracted from the directed flow is further tested with the global polarization of $\mathrm{\ensuremath{\Lambda}}$ and $\overline{\mathrm{\ensuremath{\Lambda}}}$ within the same theoretical framework, where we obtain a reasonable description of these hyperon polarization observed at different collision energies at RHIC.