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The rare decays $B^+\to K^+ \mu\bar \mu$ and $B^0\to K^{*0} \mu\bar\mu$provide the strongest constraints on the mixing of a light scalar with theHiggs boson for GeV-scale masses. The constraints sensitively depend on thebranching ratio to muons. Additional decay channels like an invisible partialwidth may substantially weaken the constraints. This scenario will be probed atBelle II in $B\to K^{(*)} + \mathrm{inv}$. We illustrate the complementarity ofscalar decays to muons and invisible decays using the currently availableresults of LHCb and BaBar. We provide two simple model realisations providing asizeable invisible scalar width, one based on a real scalar and one based on a$U(1)_{B-L}$ gauge symmetry. In both examples the scalar decays into heavyneutral leptons which can be motivated by the seesaw mechanism for neutrinomasses.

Complementarity of $B\to K^{(*)} \mu \bar \mu$ and $B\to K^{(*)} + \mathrm{inv}$ for searches of GeV-scale Higgs-like scalars

Complementarity of $B\to K^{()} \mu \bar \mu$ and $B\to K^{()} + \mathrm{inv}$ for searches of GeV-scale Higgs-like scalars