Search for the lepton-flavour violating decays B ⁰ → K ^*0 τ ^± μ ^∓

A first search for the lepton-flavour violating decays B ⁰ → K ^*0 τ ^± μ ^∓ 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 B(B0→K∗0τ+μ−)<1.0(1.2)×10−5 and B(B0→K∗0τ−μ+)<8.2(9.8)×10−6 at the 90% (95%) confidence level. [Figure not available: see fulltext.]