Differential measurement of global polarization of $Λ$, $Ξ$, and $Ω$ hyperons in Au+Au collisions at $\sqrt{s_{\mathrm{NN}}}=7.7$--$27~\mathrm{GeV}$ from the RHIC Beam Energy Scan-II

We present high-precision differential measurements of the global polarization of $Λ$, $Ξ$, and $Ω$ hyperons in Au+Au collisions at $\sqrt{s_{\mathrm{NN}}}=7.7$, $9.2$, $11.5$, $14.6$, $17.3$, $19.6$, and $27~\mathrm{GeV}$ from the RHIC Beam Energy Scan Phase II (BES-II) using the STAR detector. The results show a clear centrality dependence, with polarization increasing toward more peripheral collisions. Within the present experimental precision, no significant dependence on transverse momentum is observed for $Λ$ and $Ξ$, and no significant rapidity dependence is observed for the $Ξ$. The polarization of $Ξ$ hyperons is comparable at the current precision to that of $Λ$ hyperons, consistent with a picture in which all hyperons acquire polarization from the same global angular momentum source, with differences arising from quark content and hadronization dynamics. These high-precision, differential measurements across centrality and $p_T$ over the measured energy ranges provide a unique test of spin--vorticity coupling and sensitivity to spin--spin correlations among hyperons with different quark content (uds, dss, and sss). The results are consistent, within current precision and under the stated spin-transfer assumptions, with a common vorticity-driven polarization mechanism across strange and multistrange hyperons. Consequently, they constrain the interplay of vorticity, magnetic fields, and quark-flavor dynamics in the produced medium.