We present a measurement of the ratio of the top-quark branching fractions $R=\mathcal{B}(t\to Wb)/\mathcal{B}(t\to Wq)$, where $q$ represents quarks of type $b$, $s$, or $d$, in the final state with a lepton and hadronic jets. The measurement uses $\sqrt{s}=1.96\mathrm{TeV}$ proton-antiproton collision data from $8.7{\mathrm{fb}}^{-1}$ of integrated luminosity collected with the Collider Detector at Fermilab during Run II of the Tevatron. We simultaneously measure $R=0.94\pm 0.09$ ($\mathrm{stat}+\mathrm{syst}$) and the $t\overline{t}$ production cross section ${\sigma }_{t\overline{t}}=7.5\pm 1.0(\mathrm{stat}+\mathrm{syst})\mathrm{pb}$. The magnitude of the Cabibbo-Kobayashi-Maskawa matrix element, $|V_{\mathrm{tb}}|=0.97\pm 0.05$ ($\mathrm{stat}+\mathrm{syst}$) is extracted assuming three generations of quarks, and a lower limit of $|V_{\mathrm{tb}}|>0.89$ at 95% credibility level is set.

• Received 25 March 2013

DOI:https://doi.org/10.1103/PhysRevD.87.111101