Probing Strangeness Canonical Ensemble with $K^{-}$, $\phi(1020)$ and $\Xi^{-}$ Production in Au+Au Collisions at ${\sqrt{s_{\rm NN}} = \rm{3\,GeV}}$

We report on the first multi-differential measurement of $\phi$ meson and $\Xi^{-}$ hyperon production as well as the $\phi/K^-$ and $\phi/\Xi^-$ ratio in Au+Au collisions at ${\sqrt{s_{\rm NN}} = \rm{3\,GeV}}$ with the STAR experiment under its fixed targ et configuration at RHIC. $\phi$ mesons and $\Xi^{-}$ hyperons are measured through their hadronic decay channels, $\phi\rightarrow K^+K^-$ and $\Xi^-\rightarrow \Lambda\pi^-$. The transverse kinetic energy spectra of $K^-$, $\phi$ and $\Xi^{-}$ are presented in different centrality and rapidity intervals. The total production yields and the ratios within a $4\pi$ coverage are calculated and compared to thermal model predictions. A calculation within the grand canonical ensemble framework shows a clear discrepancy from our measurement. Our data favor the canonical ensemble approach employing local strangeness conservation with a small strangeness correlation length ($r_c \leq 4.2$ fm) in 0--10% central Au+Au collisions at ${\sqrt{s_{\rm NN}} = \rm{3\,GeV}}$.