Directed flow of $\Lambda$ in high-energy heavy-ion collisions and $\Lambda$ potential in dense nuclear matter

We investigate the sensitivity of the $\Lambda$ directed flow to the $\Lambda$ potential in mid-central Au + Au collisions at $\sqrt{s_{NN}}\approx3.0$--$30$ GeV. The $\Lambda$ potential obtained from the chiral effective field theory ($\chi$EFT) is used in a microscopic transport model, a vector version of relativistic quantum molecular dynamics (RQMDv). We find that the density-dependent $\Lambda$ potentials, obtained from the $\chi$EFT assuming weak momentum dependence of the potential, reproduce the rapidity and the beam-energy dependence of the $\Lambda$ directed flow measured by the STAR collaboration in the Beam Energy Scan program. Although the $\Lambda$ directed flow is insensitive to the density dependence of the potential, it is susceptible to the momentum dependence. We also show that a hydrodynamics picture based on the blast-wave model predicts a similarity of the proton, $\Lambda$, and $\Xi$ directed flows, but the directed flow of $\Omega$ baryons slightly deviates from other baryons. We also show that the quark coalescence predicts different rapidity dependence of the directed flows for hyperons. These investigations suggest that measurements of a wide range of the rapidity dependence of the directed flow of hyperons may provide important information about the properties of hot and dense matter created in high-energy heavy-ion collisions.Comment: 11 pages, 9 figure