  Leptons with essentially the same properties apart from their mass are
grouped into three families (or flavours). The number of leptons of each
flavour is conserved in interactions, but this is not imposed by fundamental
principles. Since the formulation of the standard model of particle physics,
the observation of flavour oscillations among neutrinos has shown that lepton
flavour is not conserved in neutrino weak interactions. So far, there has been
no experimental evidence that this also occurs in interactions between charged
leptons. Such an observation would be a sign for undiscovered particles or a
yet unknown type of interaction. Here, the ATLAS experiment at the Large Hadron
Collider at CERN reports a constraint on lepton-flavour-violating effects in
weak interactions, searching for $Z$-boson decays into a $\tau$ lepton and
another lepton of different flavour with opposite electric charge. The
branching fractions for these decays are measured to be less than
$8.1\times10^{-6}$ ($e\tau$) and $9.5\times10^{-6}$ ($\mu\tau$) at 95%
confidence level using 139 fb$^{-1}$ of proton-proton collision data at a
centre-of-mass energy $\sqrt{s}=13$ TeV and 20.3 fb$^{-1}$ at $\sqrt{s}=8$ TeV.
These results supersede the limits from the Large Electron-Positron Collider
experiments conducted more than two decades ago.
