Precise test of lepton flavour universality in $W$ -boson decays into muons and electrons in $\mathrm{pp}$ collisions at $\sqrt{s}=13\phantom{\rule{0.166667em}{0ex}}\text{Te}\phantom{\rule{-1.00006pt}{0ex}}\text{V}$ with the ATLAS detector

The ratio of branching ratios of the W boson to muons and electrons, ${R}_{W}^{\phantom{\rule{0.166667em}{0ex}}\mu /e}=B\left(W\to \mu \nu \right)$ / $B\left(W\to e\nu \right)$ , has been measured using $140\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.333333em}{0ex}}{\text{fb}}^{-1}\phantom{\rule{0.166667em}{0ex}}$ of pp collision data at $\sqrt{s}=13$ $\text{Te}\phantom{\rule{-1.00006pt}{0ex}}\text{V}$ collected with the ATLAS detector at the LHC, probing the universality of lepton couplings. The ratio is obtained from measurements of the $t\overline{t}$ production cross-section in the ee, $e\mu $ and $\mu \mu $ dilepton final states. To reduce systematic uncertainties, it is normalised by the square root of the corresponding ratio ${R}_{Z}^{\phantom{\rule{0.166667em}{0ex}}\mu \mu /ee}$ for the Z boson measured in inclusive $Z\to ee$ and $Z\to \mu \mu $ events. By using the precise value of ${R}_{Z}^{\phantom{\rule{0.166667em}{0ex}}\mu \mu /ee}$ determined from ${e}^{+}{e}^{-}$ colliders, the ratio ${R}_{W}^{\phantom{\rule{0.166667em}{0ex}}\mu /e}$ is determined to be $\begin{array}{cc}{R}_{W}^{\phantom{\rule{0.166667em}{0ex}}\mu /e}& =0.9995±0.0022\phantom{\rule{0.166667em}{0ex}}\left(\mathrm{stat}\right)\phantom{\rule{0.166667em}{0ex}}±0.0036\phantom{\rule{0.166667em}{0ex}}\left(\mathrm{syst}\right)\\ & \phantom{\rule{1em}{0ex}}±0.0014\phantom{\rule{0.166667em}{0ex}}\left(\mathrm{ext}\right).\end{array}$ The three uncertainties correspond to data statistics, experimental systematics and the external measurement of ${R}_{Z}^{\phantom{\rule{0.166667em}{0ex}}\mu \mu /ee}$ , giving a total uncertainty of 0.0045, and confirming the Standard Model assumption of lepton flavour universality in W-boson decays at the 0.5% level.