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

A first search for the lepton-flavour violating decays $B^0\to K^{\ast 0}{\tau }^{\pm }{\mu }^{\mp }$ is presented. The analysis is performed using a sample of proton-proton collision data, collected with the LHCb detector at centre-of-mass energies of 7, 8 and 13 TeV between 2011 and 2018, corresponding to an integrated luminosity of 9 fb${}^{-1}$. No significant signal is observed, and upper limits on the branching fractions are determined to be $\mathcal{B}(B^0\to K^{\ast 0}{\tau }^{+}{\mu }^{-})<1.0$ $(1.2)\times {10}^{-5}$ and $\mathcal{B}(B^0\to K^{\ast 0}{\tau }^{-}{\mu }^{+})<8.2$ $(9.8)\times {10}^{-6}$ at the 90% (95%) confidence level.