Search for the lepton-flavour violating decays $B^0 \to K^{*0} τ^\pm μ^\mp$

Abstract: A first search for the lepton-flavour violating decays $B^0 \to K^{*0} \tau^\pm \mu^\mp$ 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 ${\cal{B}}(B^0 \to K^{*0} \tau^+ \mu^-)< 1.0$ $(1.2)\times 10^{-5} $ and ${\cal{B}}(B^0 \to K^{*0} \tau^- \mu^+)< 8.2$ $(9.8) \times 10^{-6}$ at the 90% (95%) confidence level.