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A search for lepton flavour violating decays of the Higgs boson in the$\mu\tau$ and e$\tau$ decay modes is presented. The search is based on a dataset corresponding to an integrated luminosity of 35.9 fb$^{-1}$ ofproton-proton collisions collected with the CMS detector in 2016, at acentre-of-mass energy of 13 TeV. No significant excess over the standard modelexpectation is observed. The observed (expected) upper limits on the leptonflavour violating branching fractions of the Higgs boson are$\mathcal{B}$(H$\to\mu\tau$) < 0.25% (0.25%) and $\mathcal{B}$(H$\to$e$\tau$) <0.61% (0.37%), at 95% confidence level. These results are used to derive upperlimits on the off-diagonal $\mu\tau$ and e$\tau$ Yukawa couplings$\sqrt{|{Y_{\mu\tau}}|^{2}+|{Y_{\tau\mu}}|^{2}} < 1.43 \times 10^{-3}$ and$\sqrt{|{Y_{\mathrm{e}\tau}}|^{2}+|{Y_{\tau\mathrm{e}}}|^{2}} < 2.26 \times10^{-3}$ at 95% confidence level. The limits on the lepton flavour violatingbranching fractions of the Higgs boson and on the associated Yukawa couplingsare the most stringent to date.

Search for lepton flavour violating decays of the Higgs boson to $\mu\tau$ and e$\tau$ in proton-proton collisions at $\sqrt{s}=$ 13 TeV