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$b\to s\tau^+\tau^-$ measurements are highly motivated for addressinglepton-flavor-universality (LFU)-violating puzzles such as $R_{K^{(\ast)}}$anomalies. The anomalies of $R_{D^{(*)}}$ and $R_{J/\psi}$ further strengthentheir necessity and importance, given that the LFU-violating hints from bothinvolve the third-generation leptons directly. $Z$ factories at the future$e^-e^+$ colliders stand at a great position to conduct such measurementsbecause of their relatively high production rates and reconstructionefficiencies for $B$ mesons at the $Z$ pole. To fully explore this potential,we pursue a dedicated sensitivity study in four $b\to s\tau^+\tau^-$ benchmarkchannels, namely $B^0\to K^{\ast 0} \tau^+ \tau^-$, $B_s\to\phi \tau^+ \tau^-$,$B^+ \to K^+ \tau^+ \tau^- $ and $B_s \to \tau^+ \tau^-$, at the future $Z$factories. We develop a fully tracker-based scheme for reconstructing thesignal $B$ mesons and introduce a semi-quantitative method for estimating theirmajor backgrounds. The simulations indicate that branching ratios of the firstthree channels can be measured with a precision $\sim \mathcal O(10^{-7} -10^{-6})$ and that of $B_s \to \tau^+ \tau^-$ with a precision $\sim \mathcalO(10^{-5})$ at Tera-$Z$. The impacts of luminosity and tracker resolution onthe expected sensitivities are explored. The interpretations of these resultsin effective field theory are also presented.

$b\to s\tau^+\tau^-$ Physics at Future $Z$ Factories