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 13TeV 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(B^0 -> K^(*0)τ^(+)µ^(-)) < 1.0 (1.2) x 10^(-5) and B(B^0 -> K^(*0)τ^(-)µ^(+)) < 8.2 (9.8) x 10^(-6) at the 90% (95%) confidence level.