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We present a measurement of the ratio of the top-quark branching fractions$R=\mathcal{B}(t\rightarrow Wb)/\mathcal{B}(t\rightarrow Wq)$, where $q$represents quarks of type  $b$, $s$, or $d$, in the final state with a lepton and hadronic jets. Themeasurement uses $\sqrt{s}$ = 1.96 TeV proton--antiproton collision data from8.7 fb$^{-1}$ of integrated luminosity collected with the Collider Detector atFermilab during Run II of the Tevatron. We simultaneously measure $R=0.94 \pm0.09$ (stat+syst), the $t\bar{t}$ production cross section $\sigma_{t \bar t} =7.5 \pm 1.0$ (stat+syst) pb. The magnitude of the Cabibbo-Kobayashi-Maskawamatrix element, $|V_{tb}| = 0.97 \pm 0.05$ (stat+syst) is extracted assumingthree generations of quarks, and a lower limit of $|V_{tb}|>0.89$ at 95%credibility level is set.

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

Measurement of R = \boldmath${\mathcal{B}(t \rightarrow  Wb)/\mathcal{B}(t \rightarrow Wq)} $ in Top--quark--pair Decays using  Lepton+jets Events and the Full CDF Run II Data set