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Abstract

A simultaneous measurement of the three components of the top-quark and top-antiquark polarisation vectors in $t$-channel single-top-quark production is presented. This analysis is based on data from proton--proton collisions at a centre-of-mass energy of 13 TeV corresponding to an integrated luminosity of 139 fb$^{-1}$, collected with the ATLAS detector at the LHC. Selected events contain exactly one isolated electron or muon, large missing transverse momentum and exactly two jets, one being $b$-tagged. Stringent selection requirements are applied to discriminate $t$-channel single-top-quark events from the background contributions. The top-quark and top-antiquark polarisation vectors are measured from the distributions of the direction cosines of the charged-lepton momentum in the top-quark rest frame. The three components of the polarisation vector for the selected top-quark event sample are $P_{x'} =0.01\pm0.18$, $P_{y'} = -0.029\pm0.027$, $P_{z'} =0.91\pm0.10$ and for the top-antiquark event sample they are $P_{x'} = -0.02\pm0.20$, $P_{y'} = -0.007\pm0.051$, $P_{z'} = -0.79\pm 0.16$. Normalised differential cross-sections corrected to a fiducial region at the stable-particle level are presented as a function of the charged-lepton angles for top-quark and top-antiquark events inclusively and separately. These measurements are in agreement with Standard Model predictions. The angular differential cross-sections are used to derive bounds on the complex Wilson coefficient of the dimension-six $\mathcal{O}_{tW}$ operator in the framework of an effective field theory. The obtained bounds are $C_{tW} \in\ [-0.9,1.4]$ and $C_{itW} \in [-0.8,0.2]$, both at 95\% confidence level.