We measure the polarization of $W$ bosons from top-quark ($t$) decays into final states with a charged lepton and jets, $t\overline{t}\to W^{+}b{W}^{-}\overline{b}\to \ell \nu bq{\overline{q}}^{\prime }\overline{b}$, using the full Run II data set collected by the CDF II detector, corresponding to an integrated luminosity of $8.7{\mathrm{fb}}^{-1}$. A model-independent method simultaneously determines the fraction of longitudinal ($f_0$) and right-handed ($f_{+}$) $W$ bosons to yield $f_0=0.726\pm 0.066(\mathrm{stat})\pm 0.067(\mathrm{syst})$ and $f_{+}=-0.045\pm 0.044(\mathrm{stat})\pm 0.058(\mathrm{syst})$ with a correlation coefficient of $-0.69$. Additional results are presented under various standard model assumptions. No significant discrepancies with the standard model are observed.

• Received 20 November 2012

DOI:https://doi.org/10.1103/PhysRevD.87.031104