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The discrepancies between $b\to s\ell^+\ell^-$ data and the correspondingStandard Model predictions constitute the most significant hints for newphysics (at the TeV scale or below) currently available. In fact, manyscenarios that can account for these anomalies have been proposed in theliterature. However, only a single light new physics explanation, i.e. with amass below the $B$ meson scale, is possible: a light $Z^\prime$ boson. In thisarticle, we point out that improved limits on $B\to K^{(*)}\nu\nu$, includingthe experimental sensitivities required for a proper treatment of thenecessarily sizable $Z^\prime$ width, together with the forthcoming Belle~IIanalyses of $e^+e^-\to\mu^+\mu^-+{\rm invisible}$, can rule out a $Z^\prime$explanation of $b\to s\ell^+\ell^-$ data with a mass below $\approx4\,$GeV.Importantly, such a light $Z^\prime$ is the only viable single particlesolution to the $b\to s\ell^+\ell^-$ anomalies predicting $R(K^{(*)})>0$ inhigh $q^2$ bins, therefore providing an essential consistency test of data.

Towards excluding a light $Z^\prime$ explanation of $b\to s\ell^+\ell^-$