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A search for the lepton-flavour violating decays $B^0_s \to e^{\pm} \mu^{\mp}$ and $B^0 \to e^{\pm} \mu^{\mp}$ is performed with a data sample, corresponding to an integrated luminosity of 1.0 fb$^{-1}$ of $pp$ collisions at $\sqrt{s} = 7$ TeV, collected by the LHCb experiment.
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