LHC sensitivity to<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>h</mml:mi><mml:mo>→</mml:mo><mml:msup><mml:mi>τ</mml:mi><mml:mo mathvariant="bold">±</mml:mo></mml:msup><mml:msup><mml:mi>μ</mml:mi><mml:mo mathvariant="bold">∓</mml:mo></mml:msup></mml:math>

We study the sensitivity of the LHC, with $20\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of data, to lepton flavor-violating Higgs boson decays $h\ensuremath{\rightarrow}{\ensuremath{\tau}}^{\ifmmode\pm\else\textpm\fi{}}{\ensuremath{\mu}}^{\ensuremath{\mp}}$ (and $h\ensuremath{\rightarrow}{\ensuremath{\tau}}^{\ifmmode\pm\else\textpm\fi{}}{e}^{\ensuremath{\mp}}$). We consider the large population of Higgses produced in gluon fusion, combined with leptonic decays of the $\ensuremath{\tau}$, and estimate that the LHC could set a 95% confidence level bound $\mathrm{BR}(h\ensuremath{\rightarrow}{\ensuremath{\tau}}^{\ifmmode\pm\else\textpm\fi{}}{\ensuremath{\mu}}^{\ensuremath{\mp}})&lt;4.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$. This corresponds to a coupling of the order of the Cheng-Sher ansatz ${y}_{\ensuremath{\tau}\ensuremath{\mu}}=\sqrt{{m}_{\ensuremath{\tau}}{m}_{\ensuremath{\mu}}/{v}^{2}}$.