A search for the rare decays $B^0_s tomu^+mu^-$ and $B^0 tomu^+mu^-$ is performed at the LHCb experiment. The data analysed correspond to an integrated luminosity of 1 fb$^{-1}$ of $pp$ collisions at a centre-of-mass energy of 7 TeV and 2 fb$^{-1}$ at 8 TeV. An excess of $B^0_s tomu^+mu^-$ signal candidates with respect to the background expectation is seen with a significance of 4.0 standard deviations. A time-integrated branching fraction of ${cal B}(B^0_s tomu^+mu^-) = (2.9^{+1.1}_{-1.0})times 10^{-9}$ is obtained and an upper limit of ${cal B}(B^0 tomu^+mu^-) < 7.4times 10^{-10}$ at 95% confidence level is set. These results are consistent with the Standard Model expectations.
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