Measurements of electroweak penguin and lepton-flavour violating $B$ decays to final states with missing energy at Belle and Belle~II

The Belle and Belle~II experiments have accumulated a data set of $1.2{\mathrm{a}\mathrm{b}}^{-1}$ of $e^{+}{e}^{-}\to B\bar{B}$ collisions at the $\mathrm{{\rm Y}}(4S)$ resonance. Owing to the clean event environment and well-constrained initial-state kinematics, these data are ideally suited for searches for rare electroweak penguin and lepton-flavour violating $B$ decays with missing energy from neutrinos. We report results on $b\to s\nu \bar{\nu }$ processes and the interpretation, together with searches for $B\to K^{\ast 0}{\tau }^{+}{\tau }^{-}$ and for the LFV decays $B^0\to K_S^0{\tau }^{\pm }{\mathrm{\ell }}^{\mp }$ and $B^0\to K^{\ast 0}{\tau }^{\pm }{\mathrm{\ell }}^{\mp }$ ($\mathrm{\ell }=e,\mu$).