$b\to s\ddot{I}{„}^{+}\ddot{I}{„}^{-}$ Physics at Future $Z$ Factories

Abstract

$b\to s\ddot{I}{„}^{+}\ddot{I}{„}^{-}$ measurements are highly motivated for addressing lepton-flavor-universality (LFU)-violating puzzles such as $R_{K^{(\ast )}}$ anomalies. The anomalies of $R_{D^{(\ast )}}$ and $R_{J/\ddot{I}ˆ}$ further strengthen their necessity and importance, given that the LFU-violating hints from both involve the third-generation leptons directly. $Z$ factories at the future $e^{-}{e}^{+}$ colliders stand at a great position to conduct such measurements because of their relatively high production rates and reconstruction efficiencies for $B$ mesons at the $Z$ pole. To fully explore this potential, we pursue a dedicated sensitivity study in four $b\to s\ddot{I}{„}^{+}\ddot{I}{„}^{-}$ benchmark channels, namely $B^0\to K^{\ast 0}\ddot{I}{„}^{+}\ddot{I}{„}^{-}$, $B_s\to \ddot{I}•\ddot{I}{„}^{+}\ddot{I}{„}^{-}$, $B^{+}\to K^{+}\ddot{I}{„}^{+}\ddot{I}{„}^{-}$ and $B_s\to \ddot{I}{„}^{+}\ddot{I}{„}^{-}$, at the future $Z$ factories. We develop a fully tracker-based scheme for reconstructing the signal $B$ mesons and introduce a semi-quantitative method for estimating their major backgrounds. The simulations indicate that branching ratios of the first three channels can be measured with a precision $\sim \mathcal{O}(10^{-7}-10^{-6})$ and that of $B_s\to \ddot{I}{„}^{+}\ddot{I}{„}^{-}$ with a precision $\sim \mathcal{O}(10^{-5})$ at Tera-$Z$. The impacts of luminosity and tracker resolution on the expected sensitivities are explored. The interpretations of these results in effective field theory are also presented.

31 pages, 10 figures, comments welcome