Analysis of $B_s\to \ddot{I}•\hat{I}½\bar{\hat{I}}½$ at CEPC

Abstract

The rare $b\to s\hat{I}½\bar{\hat{I}}½$ 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 $b\to s\hat{I}½\bar{\hat{I}}½$ transition at a future lepton collider operating at the $Z$ pole through the $B_s\to \ddot{I}•\hat{I}½\bar{\hat{I}}½$ decay. Using the $B_s\to \ddot{I}•$ decay form factors from lattice simulations, we first update the SM prediction of BR($B_s\to \ddot{I}•\hat{I}½\bar{\hat{I}}½{)}_{\mathrm{SM}}=(9.93\pm 0.72)\times 10^{-6}$ and the corresponding $\ddot{I}•$ 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 $\ddot{I}•$ and $B_s$ reconstructions are used to suppress backgrounds. The results show that BR($B_s\to \ddot{I}•\hat{I}½\bar{\hat{I}}½)$ 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($B_s\to \ddot{I}•\hat{I}½\bar{\hat{I}}½)$ and $F_L$, the constraints on the effective theory couplings at low energy are given.

12 pages, 15 figures, 3 tables