Measurement of boldmath $R = {mathcal{B}left(t rightarrow Wb right)/mathcal{B}left(t rightarrow Wq right)} $ 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}(trightarrow Wb)/mathcal{B}(trightarrow $ $q$ 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, $left|V_{tb}right| = 0.93 pm 0.04$ (stat+syst) assuming three generations of quarks. Under these assumptions, a lower limit of $|V_{tb}|>0.85$ at 95% credibility level is set.