Search for Lepton-Flavor Violation in $Z$-Boson Decays with $\tau $ Leptons with the ATLAS Detector

A search for lepton-flavor-violating $Z\to e\tau $ and $Z\to \mu \tau $ decays with $pp$ collision data recorded by the ATLAS detector at the LHC is presented. This analysis uses $139\text{}\text{}{\mathrm{fb}}^{-1}$ of Run 2 $pp$ collisions at $\sqrt{s}=13\text{}\text{}\mathrm{TeV}$ and is combined with the results of a similar ATLAS search in the final state in which the $\tau $ lepton decays hadronically, using the same data set as well as Run 1 data. The addition of leptonically decaying $\tau $ leptons significantly improves the sensitivity reach for $Z\to \ell \tau $ decays. The $Z\to \ell \tau $ branching fractions are constrained in this analysis to $B\left(Z\to e\tau \right)<7.0×{10}^{-6}$ and $B\left(Z\to \mu \tau \right)<7.2×{10}^{-6}$ at 95% confidence level. The combination with the previously published analyses sets the strongest constraints to date: $B\left(Z\to e\tau \right)<5.0×{10}^{-6}$ and $B\left(Z\to \mu \tau \right)<6.5×{10}^{-6}$ at 95% confidence level.