Test of lepton flavour universality in $W$-boson decays into electrons and $\tau$-leptons using $pp$ collisions at $\sqrt{s}=13$ TeV with the ATLAS detector

A measurement of the ratio of the branching fractions, $R_{\tau \mathrm{/}e}=B(W\to \tau \nu )\mathrm{/}B(W\to e\nu )$, is performed using a sample of $W$ bosons originating from top-quark decays to final states containing $\tau$-leptons or electrons. This measurement uses $pp$ collisions at $\sqrt{s}=13$ TeV, collected by the ATLAS experiment at the Large Hadron Collider during Run 2, corresponding to an integrated luminosity of 140 fb${}^{-1}$. The $W\to \tau {\nu }_{\tau }$ (with $\tau \to e{\nu }_e{\nu }_{\tau }$) and $W\to e{\nu }_e$ decays are distinguished using the differences in the impact parameter distributions and transverse momentum spectra of the electrons. The measured ratio of branching fractions $R_{\tau \mathrm{/}e}=0.975\pm 0.012\text{(stat.)}\pm 0.020\text{(syst.)}$, is consistent with the Standard Model assumption of lepton flavour universality in $W$-boson decays.