Search for the lepton-flavour violating decays $B_{(s)}^0\to e^{\pm }{\mu }^{\mp }$

A search for the lepton-flavour violating decays $B^0_s \rightarrow e^\pm \mu^\mp$and$B^0 \rightarrow e^\pm \mu^\mp$ is performed based on a sample of proton-proton collision data corresponding to an integrated luminosity of 3 fb${}^{-1}$, collected with the LHCb experiment at centre-of-mass energies of 7 and 8 TeV. The observed yields are consistent with the background-only hypothesis. Upper limits on the branching fractions are determined to be $\mathcal{B}(B_s^0\to e^{\pm }{\mu }^{\mp })<5.4(6.3)\times {10}^{-9}$ and $\mathcal{B}(B^0\to e^{\pm }{\mu }^{\mp })<1.0(1.3)\times {10}^{-9}$ at $90\mathrm{\%}(95\mathrm{\%})$ confidence level, which are the strongest limits on these decays to date.