Title: Directed Flow of \bm{$\Lambda$}, \bm{$^{3}_{\Lambda}{\rm H}$}, and \bm{$^{4}_{\Lambda}{\rm H}$} in Au+Au collisions at \bm{$\sqrt{s_{NN}}$} = 3.2, 3.5, 3.9 and 4.5 GeV at RHIC

Studying hyper-nuclei production and their collectivity can shed light on their production mechanism as well as the hyperon-nucleon interactions. Heavy-ion collisions from the RHIC beam energy scan phase II (BES-II) provide an unique opportunity to understand these at high baryon densities. \\
In this presentation, we will show a systematic study on energy dependence of the directed flow for $\Lambda$ and hyper-nuclei ($^{3}_{\Lambda}{\rm H}$, $^{4}_{\Lambda}{\rm H}$) from mid-central Au+Au collisions at $\sqrt{s_{NN}}$ = 3.2, 3.5, 3.9 and 4.5 GeV, collected by the STAR experiment with the fixed-target mode during BES-II. The rapidity (y) dependence of the hyper-nuclei $v_{1}$ is studied in mid-central collisions. The extracted $v_{1}$ slopes ($dv_{1}/dy|_{y=0}$) of the hyper-nuclei are positive and decrease gradually as the collision energy increases. These hyper-nuclei results will be compared to that of light-nuclei including p, d, t/$\rm ^{3}He$ and $\rm ^{4}He$. Finally, discussions will be made using comparison to hadronic transport model including coalescence after-burner calculations.