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

This paper presents a measurement of the polarisation of $W$ bosons from $t\bar{t}$ decays, reconstructed in events with one high-$p_T$ lepton and 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 20.2 fb${}^{-1}$. The angle ${\theta }^{\ast }$ between the $b$-quark from the top quark decay and a direct $W$ boson decay product in the $W$ boson rest frame is sensitive to the $W$ boson polarisation. Two different $W$ decay products are used as polarisation analysers: the charged lepton and the down-type quark for the leptonically and hadronically decaying $W$ boson, respectively. The most precise measurement of the $W$ boson polarisation via the distribution of $\cos {\theta }^{\ast }$ is obtained using the leptonic analyser and events in which at least two of the jets are tagged as $b$-quark jets. The fitted fractions of longitudinal, left- and right-handed polarisation states are $F_{$0$}= 0.709 \pm {0.019}$,$F_{$\mathrm{L}$}= 0.299 \pm {0.015}$and$F_{$\mathrm{R}$}= -0.008 \pm {0.014}$,andarethemostpreciselymeasured$W$ boson polarisation fractions to date. Limits on anomalous couplings of the $Wtb$ vertex are set.