The combination of measurements of the W boson polarization in top quark decays performed by the ATLAS and CMS collaborations is presented. The measurements are based on proton-proton collision data produced at the LHC at a centre-of-mass energy of 8 TeV, and corresponding to an integrated luminosity of about 20 fb-1 for each experiment. The measurements used events containing one lepton and having different jet multiplicities in the final state. The results are quoted as fractions of W bosons with longitudinal (F0), left-handed (FL), or right-handed (FR) polarizations. The resulting combined measurements of the polarization fractions are F0 = 0.693 +- 0.014 and FL = 0.315 +- 0.011. The fraction FR is calculated from the unitarity constraint to be FR = -0.008 +- 0.007. These results are in agreement with the standard model predictions at next-to-next-to-leading order in perturbative quantum chromodynamics and represent an improvement in precision of 25 (29)% for F0 (FL) with respect to the most precise single measurement. A limit on anomalous right-handed vector (VR), and left- and right-handed tensor (gL; gR) tWb couplings is set while xing all others to their standard model values. The allowed regions are [-0.11; 0.16] for VR, [-0.08; 0.05] for gL, and [-0.04; 0.02] for gR, at 95% confidence level. Limits on the corresponding Wilson coefficients are also derived.
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