Precision Tests in $b\to s\ell\ell$ ($\ell=e,\mu$) at FCC-ee

The rare semi-leptonic decays $B\to K^\ast \ell^+\ell^-$, with $\ell=e, \mu$, are highly sensitive to new physics (NP) due to their suppression in the Standard Model (SM). Current LHCb measurements exhibit a significant tension with respect to state-of-the-art SM theory predictions. The proposed tera-$Z$ run at FCC-ee provides a unique opportunity to untangle the origin of this tension by producing a very large sample of $B$-mesons in a clean $e^+e^-$  environment. This note explores the expected precision of $B\to K^\ast \ell^+\ell^-$ ($\ell=e, \mu$) measurements at FCC-ee, comparing it with HL-LHC projections.