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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 ofproton-proton collision data corresponding to an integrated luminosity of 3fb$^{-1}$, collected with the LHCb experiment at centre-of-mass energies of 7and 8 TeV. The observed yields are consistent with the background-onlyhypothesis. Upper limits on the branching fractions are determined to be$\mathcal{B}(B^0_s \rightarrow e^\pm \mu^\mp) < 5.4\,(6.3) \times 10^{-9}$ and$\mathcal{B}(B^0 \rightarrow e^\pm \mu^\mp) < 1.0\,(1.3) \times 10^{-9}$ at$90\%\,(95\%)$ confidence level, which are the strongest limits on these decaysto date.

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