Combination of the ATLAS and CMS measurements of the W-boson polarization in top-quark decays

This note describes the combination of recent measurements of the W-boson polarization in top-quark decays performed by the ATLAS and CMS Collaborations. The measurements are based on proton-proton collision data corresponding to integrated luminosities ranging from 35 pb$^{-1}$ to 2.2 fb$^{-1}$ produced at the LHC at a center-of-mass energy of $\sqrt{s}=7\, \mathrm{TeV}$. The results are quoted as helicity fractions, i.e.~the fractions of events which contain W bosons with longitudinal and left-handed polarization. he combined helicity fractions are \begin{align*} F_{0} & = 0.626 \pm 0.034~\textrm{(stat.)} \pm 0.048~\textrm{(syst.)}\, , \\ F_{L} & = 0.359 \pm 0.021~\textrm{(stat.)} \pm 0.028~\textrm{(syst.)}\, , \end{align*} which are in agreement with predictions from NNLO QCD. The fraction of W bosons with right-handed polarization is calculated assuming the sum of all fractions to be unity: \begin{align*} F_{R} & = 0.015 \pm 0.034\, , \end{align*} where the uncertainty includes the statistical and systematic uncertainties. Exclusion limits on anomalous Wtb couplings are derived from these results.