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This paper presents a measurement of the polarisation of $W$ bosons from$t\bar{t}$ decays, reconstructed in events with one high-$p_{\mbox{T}}$ leptonand at least four jets. Data from $pp$ collisions at the LHC were collected at$\sqrt{s}$ = 8 TeV and correspond to an integrated luminosity of 20.2fb$^{-1}$. The angle $\theta^{*}$ between the $b$-quark from the top quarkdecay and a direct $W$ boson decay product in the $W$ boson rest frame issensitive to the $W$ boson polarisation. Two different $W$ decay products areused as polarisation analysers: the charged lepton and the down-type quark forthe leptonically and hadronically decaying $W$ boson, respectively. The mostprecise measurement of the $W$ boson polarisation via the distribution of$\cos{\theta^{*}}$ is obtained using the leptonic analyser and events in whichat least two of the jets are tagged as $b$-quark jets. The fitted fractions oflongitudinal, left- and right-handed polarisation states are $F_{\mathrm{0}}=0.709 \pm {0.019}$, $F_{\mathrm{L}}= 0.299 \pm {0.015}$ and $F_{\mathrm{R}}=-0.008 \pm {0.014}$, and are the most precisely measured $W$ boson polarisationfractions to date. Limits on anomalous couplings of the $Wtb$ vertex are set.

Measurement of the $W$ boson polarisation in $t\bar{t}$ events from $pp$ collisions at $\sqrt{s}$ = 8 TeV in the lepton+jets channel with ATLAS