Search for lepton-flavor-violating decays of the $Z$ boson into a $\tau$-lepton and a light lepton with the ATLAS detector

Lepton flavour violation in the charged lepton sector is an unambiguous signal of physics beyond the Standard Model. Searches for lepton flavour violation in decays of the $Z$ boson with the ATLAS detector is reported, focusing on decays into an electron or muon and a hadronically decaying $\tau$-lepton, using $pp$ collisions data with a centre-of-mass energy of 13 TeV. Upper limits on the branching ratios of lepton-flavor-violating decays are set at the 95% confidence level: $\mathcal{B}(Z\to e\tau)<5.8\times10^{-5}$ and $\mathcal{B}(Z\to \mu\tau)<2.4\times10^{-5}$. When combined with a previous ATLAS result based on $pp$ collisions data with a centre-of-mass energy of 8 TeV, an upper limit of $\mathcal{B}(Z\to \mu\tau)<1.3\times10^{-5}$ is obtained.