Motivated by a recent Belle~II measurement that suggests an excess in the rare decay $B \to K\, E_{ \rm miss}$, and building upon our recent differential decay rate likelihood analysis of the existing experimental information, we investigate possible new physics (NP) scenarios in which light invisible states participate in flavour-changing $b \to s$ transitions. In particular, we consider the total and differential $B\to K^* E_{ \rm miss}$ decay rates and $K^*$ polarisation effects in each NP scenario preferred by the $B\to K E_{ \rm miss}$ measurement. We show that future measurements of these $B \to K^* E_{ \rm miss}$ observables will offer decisive discrimination among the different NP explanations. Our results highlight the strong complementarity of the rare semi-invisible $b$-hadron decay observables, and underline the importance of analysing their momentum transfer spectra when probing extensions of the Standard Model that feature new light degrees of freedom.
Categories: hep-ph hep-ex