We report measurements of the polarization of $W$ bosons from top-quark decays using 2.7 ${\mathrm{fb}}^{-1}$ of $p\overline{p}$ collisions collected by the CDF II detector. Assuming a top-quark mass of $175\mathrm{GeV}/c^2$, three measurements are performed. A simultaneous measurement of the fraction of longitudinal ($f_0$) and right-handed ($f_{+}$) $W$ bosons yields the model-independent results $f_0=0.88\pm 0.11(\mathrm{stat})\pm 0.06(\mathrm{syst})$ and $f_{+}=-0.15\pm 0.07(\mathrm{stat})\pm 0.06(\mathrm{syst})$ with a correlation coefficient of $-0.59$. A measurement of $f_0$ [$f_{+}$] constraining $f_{+}$ [$f_0$] to its standard model value of 0.0 [0.7] yields $f_0=0.70\pm 0.07(\mathrm{stat})\pm 0.04(\mathrm{syst})$ [$f_{+}=-0.01\pm 0.02(\mathrm{stat})\pm 0.05(\mathrm{syst})$]. All these results are consistent with standard model expectations. We achieve the single most precise measurements of $f_0$ for both the model-independent and model-dependent determinations.

• Received 2 March 2010

DOI:https://doi.org/10.1103/PhysRevLett.105.042002