The rare $b\to s\nu\bar{ \nu}$ decays are sensitive to contributions of new physics (NP) and helpful to resolve the puzzle of multiple $B$ flavor anomalies. In this work, we propose to study the $b\to s\nu\bar{ \nu}$ transition at a future lepton collider operating at the $Z$ pole through the $B_s \to \phi\nu\bar{ \nu}$ decay. Using the $B_s\to\phi$ decay form factors from lattice simulations, we first update the SM prediction of BR($B_s \to \phi\nu\bar{ \nu})_{ \mathrm{ SM}}=(9.93\pm 0.72)\times 10^{ -6}$ and the corresponding $\phi$ longitudinal polarization fraction $F_{ L,{ \mathrm{ SM}}}=0.53\pm 0.04$. Our analysis uses the full CEPC simulation samples with a net statistic of $\mathcal{ O}(10^9)$ $Z$ decays. Precise $\phi$ and $B_s$ reconstructions are used to suppress backgrounds. The results show that BR($B_s \to \phi\nu\bar{ \nu})$ can be measured with a statistical uncertainty of $\mathcal{ O}(\%)$ and an $S/B$ ratio of $\mathcal{ O}(1)$ at the CEPC. The quality measures for the event reconstruction are also derived. By combining the measurement of BR($B_s \to \phi\nu\bar{ \nu})$ and $F_L$, the constraints on the effective theory couplings at low energy are given.
Categories: hep-ph hep-ex