Global $\Lambda$ polarization in heavy-ion collisions at high baryon density

Based on the model of three-fluid dynamics (3FD), the global $\Lambda$ polarization ($P_\Lambda$) is calculated in Au+Au collisions at 3 $\leq\sqrt{s_{NN}}\leq$ 9 GeV, in which high baryon density is achieved. Various contributions to $P_\Lambda$ are considered: those from the thermal vorticity, meson field, thermal shear and spin-Hall effect. Feed-down from higher-lying resonances is also taken into account. The results are compared with available data. Special attention is payed to the collision energies of $\sqrt{s_{NN}}=$ 3, 3.2, 3.5, 3.9, and 4.5 GeV, for which a thorough scan of the energy, rapidity, and centrality dependence of $P_\Lambda$ is performed. The results for 3 GeV reasonably well reproduce the corresponding STAR data. While the results at $\sqrt{s_{NN}}=$ 3.2, 3.5, 3.9, and 4.5 GeV can be considered as predictions for results of measurements within the STAR fixed-target (STAR-FXT) programthat are expected in the nearest future. It is predicted that a broad maximum of $P_\Lambda$ is reached at $\sqrt{s_{NN}}\approx$ 3--3.9 GeV, exact position of which depends on the centrality and width of the midrapidity range of observation. Impact of the meson-field, thermal-shear and spin-Hall-effect contributions to $P_\Lambda$ is also studied.