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The current limitations of the standard model of elementary particle physics drive the search for phenomenons forbidden within that framework with the goal to unveil a more universal theory. This thesis presents the search for two lepton flavour violating decays forbidden in the standard model: and . The search is performed by studying proton-proton collision data collected by the detector of the LHCb collaboration corresponding to of integrated luminosity. No significant signal is observed and as such the following upper limits at confidence level are set: $\mathcal{B}(B^{+} \rightarrow K^{+} \tau^{-} \mu^{+})
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