Flavor-resolved four-fermion probes at the FCC-ee $Z$ pole

The electron-positron Future Circular Collider will provide an unprecedented opportunity for precision studies at the $Z$ pole. In addition to improving the electroweak measurements pioneered at LEP, Tera-$Z$ statistics and modern jet flavor reconstruction could make rare, flavor-resolved final states accessible as precision observables. We study the exclusive four-body processes $e^{+}{e}^{-}\to Z\to Q\bar{Q}{\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-}$ with $Q=c,b$ and $\mathrm{\ell }=\mu ,\tau$ as probes of flavor-specific new physics contact interactions. A fast analysis yields representative multi-TeV reaches for vector-current interactions involving bottom or charm quarks and muons or taus, providing a baseline for future detector-level studies. For charm-current interactions, the projected direct sensitivities are comparable to those obtained indirectly from electroweak precision observables. Two-dimensional fits further show that these processes retain quark-flavor information that can be poorly resolved by the renormalization-group-induced electroweak response. These results illustrate how flavor-resolved four-body $Z$ processes can bridge the electroweak and flavor programs at FCC-ee, opening a new class of complementary precision observables.