The first direct search for lepton-flavour-violating decays of the recently discovered Higgs boson (H) is described. The search is performed in the H →μτeand H →μτhchannels, where τeand τhare tau leptons reconstructed in the electronic and hadronic decay channels, respectively. The data sample used in this search was collected in pp collisions at a centre-of-mass energy of √s=8TeVwith the CMS experiment at the CERN LHC and corresponds to an integrated luminosity of 19.7fb−1. The sensitivity of the search is an order of magnitude better than the existing indirect limits. A slight excess of signal events with a significance of 2.4 standard deviations is observed. The p-value of this excess at MH=125GeVis 0.010. The best fit branching fraction is B(H →μτ) =(0.84+0.39−0.37)%. A constraint on the branching fraction, B(H →μτ) \u3c1.51%at 95% confidence level is set. This limit is subsequently used to constrain the μ–τYukawa couplings to be less than 3.6 ×10−3
