  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
($F_0$), left-handed ($F_\mathrm{L}$), or right-handed ($F_\mathrm{R}$)
polarizations. The resulting combined measurements of the polarization
fractions are $F_0 =$ 0.693 $\pm$ 0.014 and $F_\mathrm{L} =$ 0.315 $\pm$ 0.011.
The fraction $F_\mathrm{R}$ is calculated from the unitarity constraint to be
$F_\mathrm{R} = -$0.008 $\pm$ 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 $F_0$ ($F_\mathrm{L}$) with respect to the most precise single measurement.
A limit on anomalous right-handed vector ($V_{\text{R}}$), and left- and
right-handed tensor ($g_{\text{L}},g_{\text{R}}$) tWb couplings is set while
fixing all others to their standard model values. The allowed regions are
[$-$0.11, 0.16] for $V_{\text{R}}$, [$-$0.08, 0.05] for $g_{\text{L}}$, and
[$-$0.04, 0.02] for $g_{\text{R}}$, at 95% confidence level. Limits on the
corresponding Wilson coefficients are also derived.
