A search is presented for a Higgs-like boson with mass in the range 45 to 195 GeV/$c^2$ decaying into a muon and a tau lepton. The dataset consists of proton-proton interactions at a centre-of-mass energy of 8 TeV, collected by the LHCb experiment, corresponding to an integrated luminosity of 2 fb$^{-1}$. The tau leptons are reconstructed in both leptonic and hadronic decay channels. An upper limit on the production cross-section multiplied by the branching fraction at 95% confidence level is set and ranges from 22 pb for a boson mass of 45 GeV/$c^2$ to 4 pb for a mass of 195 GeV/$c^2$.
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