Measurement of \boldmath $R=\mathcal{B}(t\to Wb)\mathrm{/}\mathcal{B}(t\to Wq)$ in Top--Quark--Pair Decays using Dilepton Events and the Full CDF Run II Data Set

We present a measurement of the ratio of the top-quark branching fractions $R=\mathcal{B}(t\to Wb)\mathrm{/}\mathcal{B}(t\to$ $q$ represents quarks of flavors $b$, $s$, or $d$, in the final state, in events with two charged leptons, missing transverse energy and at least two jets. The measurement uses $\sqrt{s}$ = 1.96 TeV proton–antiproton collision data corresponding to an integrated luminosity of 8.7 fb${}^{-1}$ and collected with the Collider Detector at Fermilab during Run II of the Tevatron. We measure $R=0.87\pm 0.07$ (stat+syst), and extract the magnitude of the Cabibbo-Kobayashi-Maskawa matrix element, $\mid V_{tb}\mid =0.93\pm 0.04$ (stat+syst) assuming three generations of quarks. Under these assumptions, a lower limit of $\mathrm{\mid }{V}_{tb}\mathrm{\mid }>0.85$ at 95% credibility level is set.