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

A search for the lepton-flavour violating decays $B^0\to K^{\ast 0}{\mu }^{\pm }{e}^{\mp }$ and $B_s^0\to \phi {\mu }^{\pm }{e}^{\mp }$ is presented, using proton-proton collision data collected by the LHCb detector at the LHC, corresponding to an integrated luminosity of $9{\text{fb}}^{-1}$. No significant signals are observed and upper limits of \begin{align} {\cal B}( B^0 \to K^{*0} μ^+ e^- ) &< \phantom{1}5.7\times 10^{-9}~(6.9\times 10^{-9}),\newline {\cal B}( B^0 \to K^{*0} μ^- e^+ ) &< \phantom{1}6.8\times 10^{-9}~(7.9\times 10^{-9}),\newline {\cal B}( B^0 \to K^{*0} μ^\pm e^\mp ) &< 10.1\times 10^{-9}~(11.7\times 10^{-9}),\newline {\cal B}( B_s^0 \to φμ^\pm e^\mp ) &< 16.0\times 10^{-9}~(19.8\times 10^{-9}) \end{align} are set at $90\mathrm{\%}(95\mathrm{\%})$ confidence level. These results constitute the world’s most stringent limits to date, with the limit on the decay $B_s^0\to \phi {\mu }^{\pm }{e}^{\mp }$ the first being set. In addition, limits are reported for scalar and left-handed lepton-flavour violating New Physics scenarios.