Search for lepton flavour violating decays at LHCb

Several measurements on $b$-hadron decays suggest a deviation from the Lepton Flavour Universality property of the Standard Model.New Physics models have been proposed to coherently explain these alleged deviationsby introducing non-universal interactions mediated for example by $Z'$ bosons or leptoquarks.Since these non-universal lepton flavour couplings usually imply the non-conservation of the lepton flavour, searches for these processes are pursued by the LHCb experiment. Three recent results in this field are reported in this document: $B^0_{(s)}\to e^+\mu^-$, $B^0_{(s)}\to \tau^+\mu^-$ and $B^+\to K^+e^{\pm}\mu^{\mp}$ searches with $3$ fb$^{-1}$ of data.