Precise test of lepton flavour universality in $$\\varvec{W}$$-boson decays into muons and electrons in $$\\varvec{pp}$$ collisions at $$\\varvec{\\sqrt{s}}=13\\,\\text {T}\\text {e}\\hspace{-1.00006pt}\\text {V} $$ with the ATLAS detector

The ratio of branching ratios of the W boson to muons and electrons, $$R^{\\,\\mu /e}_W={{\\mathcal {B}}(W\\rightarrow \\mu \\nu )}$$ R W μ / e = B ( W → μ ν ) /$${{\\mathcal {B}}(W\\rightarrow e\\nu )}$$ B ( W → e ν ) , has been measured using $$140\\,\\text{ fb}^{-1}\\,$$ 140 fb - 1 of pp collision data at $$\\sqrt{s}=13$$ s = 13 $$\\text {T}\\text {e}\\hspace{-1.00006pt}\\text {V}$$ Te V collected with the ATLAS detector at the LHC, probing the universality of lepton couplings. The ratio is obtained from measurements of the $$t\\bar{t}$$ t t ¯ production cross-section in the ee, $$e\\mu $$ e μ and $$\\mu \\mu $$ μ μ dilepton final states. To reduce systematic uncertainties, it is normalised by the square root of the corresponding ratio $$R^{\\,\\mu \\mu /ee}_Z$$ R Z μ μ / e e for the Z boson measured in inclusive $$Z\\rightarrow ee$$ Z → e e and $$Z\\rightarrow \\mu \\mu $$ Z → μ μ events. By using the precise value of $$R^{\\,\\mu \\mu /ee}_Z$$ R Z μ μ / e e determined from $$e^+e^-$$ e + e - colliders, the ratio $$R^{\\,\\mu /e}_W$$ R W μ / e is determined to be $$\\begin{aligned} R^{\\,\\mu /e}_W&= 0.9995\\pm 0.0022\\,\\mathrm {(stat)}\\,\\pm 0.0036\\,\\mathrm {(syst)}\\\\ &\\quad \\pm 0.0014\\,\\mathrm {(ext)} . \\end{aligned}$$ R W μ / e = 0.9995 ± 0.0022 ( stat ) ± 0.0036 ( syst ) ± 0.0014 ( ext ) . The three uncertainties correspond to data statistics, experimental systematics and the external measurement of $$R^{\\,\\mu \\mu /ee}_Z$$ R Z μ μ / e e , 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.