The first limit on invisible decays of $B_s$ mesons comes from LEP

Motivated by the recent evidence for $B^{+}\to K^{+}\bar{\nu }\nu$ decays at Belle II, we point out that fully invisible $B_d$ and $B_s$ meson decays are strongly constrained by LEP. A reinterpretation of an old inclusive ALEPH search for $b$-hadron decays with large missing energy allows us to place the limits $\mathrm{B}\mathrm{r}(B_d\to \mathrm{i}\mathrm{n}\mathrm{v}\mathrm{i}\mathrm{s}\mathrm{i}\mathrm{b}\mathrm{l}\mathrm{e})<1.4\times {10}^{-4}$ and $\mathrm{B}\mathrm{r}(B_s\to \mathrm{i}\mathrm{n}\mathrm{v}\mathrm{i}\mathrm{s}\mathrm{i}\mathrm{b}\mathrm{l}\mathrm{e})<5.6\times {10}^{-4}$, both at $90\mathrm{\%}$ CL. The $B_d$ limit is only a factor of 6 looser than the world-leading one provided by the BaBar collaboration, while the $B_s$ one is the first limit in the literature on this decay mode. These results are relevant in the context of new light states coupled to quarks and exemplify the power of a future Tera-$Z$ factory at FCC-ee to look for $B$ meson decays containing missing energy.