Measurement of the helicity fractions ofWbosons from top quark decays using fully reconstructedtt¯events with CDF II

We present a measurement of the fractions $F_0$ and $F_{+}$ of longitudinally polarized and right-handed $W$ bosons in top-quark decays using data collected with the CDF II detector. The data set used in the analysis corresponds to an integrated luminosity of approximately $318{\mathrm{pb}}^{-1}$. We select $t\overline{t}$ candidate events with one lepton, at least four jets, and missing transverse energy. Our helicity measurement uses the decay angle ${\theta }^{*}$, which is defined as the angle between the momentum of the charged lepton in the $W$ boson rest frame and the $W$ momentum in the top-quark rest frame. The $\cos {\theta }^{*}$ distribution in the data is determined by full kinematic reconstruction of the $t\overline{t}$ candidates. We find $F_0={0.85}_{-0.22}^{+0.15}(\mathrm{stat})\pm 0.06(\mathrm{syst})$ and $F_{+}={0.05}_{-0.05}^{+0.11}(\mathrm{stat})\pm 0.03(\mathrm{syst})$, which is consistent with the standard model prediction. We set an upper limit on the fraction of right-handed $W$ bosons of $F_{+}<0.26$ at the 95% confidence level.