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A search for the rare leptonic decay $B^{+} \rightarrow {\mu}^{+}{\mu}^{-}{\mu}^{+}{\nu}_{{\mu}}$ is performed using proton-proton collision data corresponding to an integrated luminosity of fb collected by the LHCb experiment. The search is carried out in the region where the lowest of the two mass combinations is below MeV/c. The data are consistent with the background-only hypothesis and an upper limit of at 95% confidence level is set on the branching fraction in the stated kinematic region.

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