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This Letter presents direct searches for lepton flavour violation in Higgsboson decays, $H\rightarrow e\tau$ and $H\rightarrow\mu\tau$, performed withthe ATLAS detector at the LHC. The searches are based on a data sample ofproton-proton collisions at a centre-of-mass energy $\sqrt{s} = 13$ TeV,corresponding to an integrated luminosity of $36.1\,\mathrm{fb}^{-1}$. Nosignificant excess is observed above the expected background from StandardModel processes. The observed (median expected) 95 % confidence-level upperlimits on the lepton-flavour-violating branching ratios are $0.47\%$($0.34^{+0.13}_{-0.10}\,\%$) and $0.28\%$ ($0.37^{+0.14}_{-0.10}\,\%$) for$H\to e\tau$ and $H\to\mu\tau$, respectively.

Searches for lepton-flavour-violating decays of the Higgs boson in $\sqrt{s}=13$ TeV $pp$ collisions with the ATLAS detector