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Analysis of $B_s\toϕν\barν$ at CEPC

The rare $b\to sν\barν$ 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 $b\to sν\barν$ transition at a future lepton collider operating at the $Z$ pole through the $B_s \to ϕν\barν$ decay. Using the $B_s\toϕ$ decay form factors from lattice simulations, we first update the SM prediction of BR($B_s \to ϕν\barν)_{\mathrm{SM}}=(9.93\pm 0.72)\times 10^{-6}$ and the corresponding $ϕ$ 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 $ϕ$ and $B_s$ reconstructions are used to suppress backgrounds. The results show that BR($B_s \to ϕν\barν)$ 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($B_s \to ϕν\barν)$ and $F_L$, the constraints on the effective theory couplings at low energy are given.