Search for the lepton-flavour violating decays B_(s)⁰→e^±μ^∓

A search for the lepton-flavour violating decays B_s⁰→e^±μ^∓ and B⁰→e^±μ^∓ 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 fraction of the B_s⁰→e^±μ^∓ decays are evaluated both in the hypotheses of an amplitude completely dominated by the heavy eigenstate and by the light eigenstate. The results are @/@ℬ(B_s⁰→e)<6.3(5.4)×10⁻⁹ and @/@ℬ(B_s⁰→e)<7.2(6.0)×10⁻⁹ at 95% (90%) confidence level, respectively. The upper limit on the branching fraction of the B⁰ → e^±μ^∓ decay is also evaluated, obtaining @/@ℬ(B⁰→e)<1.3(1.0)×10⁻⁹ at 95% (90%) confidence level. These are the strongest limits on these decays to date.