Probing New Physics with $\mu^+ \mu^- \to bs$ at a Muon Collider

We show that bottom-strange production at a high-energy muon collider, $\mu^+ \mu^- \to b s$, is a sensitive probe of new physics. We consider the full set of four-fermion contact interactions that contribute to this process at dimension 6, and discuss the complementarity of a muon collider and of the study of rare $B$ meson decays that also probe said new physics. If a signal were to be found at a muon collider, the forward-backward asymmetry of the $b$-jet provides diagnostics about the underlying chirality structure of the new physics. In the absence of a signal at a center of mass energy of $10$~TeV, $\mu^+ \mu^- \to b s$ can indirectly probe new physics at scales close to $100$~TeV. We also discuss the impact that beam polarization has on the muon collider sensitivity performance.