Combination of the W boson polarization measurements in top quark decays using ATLAS and CMS data at $\sqrt{s}=$ 8 TeV

This paper presents the combination of measurements of the W bosons polarization in top quark decays performed by the ATLAS and CMS Collaborations. The measurements are based on proton-proton collision data produced at the LHC at a centre-of-mass energy of 8 TeV corresponding to an integrated luminosity of about 20 $fb^{-1}$ for each experiment. The measurements used events containing one lepton and different jet multiplicities in the final state. The results are quoted as fractions of events that contain W bosons with longitudinal ($F_{0}$), left-handed ($F_{L}$), or right-handed ($F_{R}$) polarizations. The resulting combined LHC measurements of the polarization fractions are $F_{0} = 0.693 \pm 0.014$ and $F_{L} = 0.315 \pm 0.011$. The fraction of W bosons with right-handed polarization is calculated from the unitarity constraint to be $F_{R} = 0.008 \pm 0.007$. The combination results are in agreement with the standard model predictions at next-to-next-to leading order in QCD and represent an improvement in precision of 25% for $F_{0}$ and 29% for $F_{L}$ with respect to the most precise single measurement. A limit on each anomalous $Wtb$ coupling is set while fixing all others to their standard model values, with the allowed regions being $[-0.11, 0.16]$ for $V_{R}$, $[-0.08, 0.05]$ for $g_{L}$, and $[-0.04, 0.02]$ for $g_{R}$, at 95\% confidence level. Limits on Wilson coefficients were also derived.