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A measurement of the polarisation of $W$ bosons produced in top-quark decaysis presented, using proton-proton collision data at a centre-of-mass energy of$\sqrt{s} = 13$ TeV. The data were collected by the ATLAS detector at the LargeHadron Collider and correspond to an integrated luminosity of 139 fb$^{-1}$.The measurement is performed selecting $t\bar{t}$ events decaying into finalstates with two charged leptons (electrons or muons) and at least two$b$-tagged jets. The polarisation is extracted from the differentialcross-section distribution of the $\cos{\theta^{*}}$ variable, where$\theta^{*}$ is the angle between the momentum direction of the charged leptonfrom the $W$ boson decay and the reversed momentum direction of the $b$-quarkfrom the top-quark decay, both calculated in the $W$ boson rest frame.Parton-level results, corrected for the detector acceptance and resolution, arepresented for the $\cos{\theta^{*}}$ angle. The measured fractions oflongitudinal, left- and right-handed polarisation states are found to be $f_{0}= 0.684 \pm 0.005\,\mathrm{(stat.)} \pm 0.014\,\mathrm{(syst.)}$,$f_{\mathrm{L}} = 0.318 \pm 0.003\,\mathrm{(stat.)} \pm0.008\,\mathrm{(syst.)}$ and $f_{\mathrm{R}} = -0.002 \pm0.002\,\mathrm{(stat.)} \pm 0.014\,\mathrm{(syst.)}$, in agreement with theStandard Model prediction.

Measurement of the polarisation of $W$ bosons produced in top-quark decays using dilepton events at $\sqrt{s} = 13$ TeV with the ATLAS experiment