Test of the universality of $\tau$ and $\mu$ lepton couplings in W boson decays from $t\bar{t}$ events at 13 TeV with the ATLAS detector

The Standard Model of particle physics constitutes our current best understanding of physics at the smallest scales. A fundamental axiom of this theory is the universality of the couplings of the different generations of leptons to the electroweak gauge bosons. The measurement of the ratio $R(\tau/\mu) = \mbox{BR}(W \to \tau \nu_\tau)/\mbox{BR}(W \to \mu \nu_\mu)$ constitutes an important test of this axiom. A measurement of this quantity from an approach using di-leptonic $t\bar{t}$ events is presented based on 139 fb${}^{-1}$ of data recorded with the ATLAS detector in the years 2015 to 2018. Muons originating from $W$ bosons and those originating via an intermediate $\tau$ are distinguished using the lifetime of the $\tau$ lepton, through the muon transverse impact parameter, and differences in the muon transverse momentum spectra. The value of $R(\tau/\mu)$ is found to be $0.992 \pm 0.013~[\pm 0.007~\textrm{(stat)}~\pm~0.011~\textrm{(syst)}]$ and therefore is in agreement with the hypothesis of universal lepton couplings as postulated in the Standard Model. This forms the most precise measurement of this ratio, and the only such measurement from the Large Hadron Collider, to date.