Search for the lepton-flavour violating decays $B_s^0 \to K^{*0} \mu^\pm e^\mp$ and \boldmath$B_s^0 \to \phi \mu^\pm e^\mp$

A search for the lepton-flavour violating decays $B^0 \to K^{*0} \mu^\pm e^\mp$ and $B_s^0 \to \phi \mu^\pm e^\mp$ is presented, using data collected by the LHCb experiment at the LHC in $pp$ collisions, corresponding to an integrated luminosity of $9\,\mathrm{fb}^{-1}$. No significant excess is observed and upper limits are set, constituting the world's most stringent limits to date. The reported limit on the decay $B_s^0 \to \phi \mu^\pm e^\mp$ is the first being set. In addition, exclusion limits are presented for scalar and left-handed lepton-flavour violating New Physics scenarios.