Lepton polarization asymmetries in rare semi-tauonic $$ b rightarrow s $$ exclusive decays at FCC- ee

We consider measurements of exclusive rare semi-tauonic b-hadron decays, mediated by the (b rightarrow s tau ^+ tau ^-) transition, at a future high-energy circular electron–positron collider (FCC-ee). We argue that the high boosts of b-hadrons originating from on-shell Z boson decays allow for a full reconstruction of the decay kinematics in hadronic (tau ) decay modes (up to discrete ambiguities). This, together with the potentially large statistics of (Zrightarrow bbar{b}), opens the door for the experimental determination of (tau ) polarizations in these rare b-hadron decays. In the light of the current experimental situation on lepton flavor universality in rare semileptonic B decays, we discuss the complementary short-distance physics information carried by the (tau ) polarizations and suggest suitable theoretically clean observables in the form of single- and double-(tau ) polarization asymmetries.