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The study of the rare decays $B\to K^{(*)} \nu \bar\nu$ offers a window intothe dynamics operating at the electroweak scale, allowing studies of theStandard Model and searches for heavy new physics. However, the analysis ofthese decays is also potentially sensitive to the on-shell production of newlight bosons $X$ through the process $B\to K^{(*)} X$. In particular, Belle~IIhas recently measured $B^+\to K^+\nu\bar\nu$, finding a $2.8\sigma$ excessunder the assumption of heavy new physics. Since this excess is ratherlocalized in the kaon energy, a fit that includes the decay mode $B^+\to K^+ X$to the kinematic distributions prefers $m_X\approx2\,$GeV with branchingfraction Br$[B\to KX]=(8.8\pm2.5)\times 10^{-6}$ and a significance of$\approx3.6\sigma$. However, no excess was found in the BaBar measurements of$B\to K^{(*)} \nu \bar\nu$, and a global analysis of the Belle II and BaBardata leads to Br$[B\to KX]=(5.1\pm2.1)\times 10^{-6}$ with a reducedsignificance of $\approx2.4\sigma$. We then study various simplifieddark-flavoured models and present a possible UV completion based on a gauged$B_3-L_3$ symmetry, highlighting the discovery potential of dedicated searchesfor $B\to K^{(*)}X$ at Belle II.

Light New Physics in $B\to K^{(*)}\nu\bar\nu$?