Measurement of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>B</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:mi>W</mml:mi><mml:mi>b</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo stretchy="false">/</mml:mo><mml:mi>B</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:mi>W</mml:mi><mml:mi>q</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math>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=B(t→Wb)/B(t→Wq), where q represents any quark flavor, in events with two charged leptons, imbalance in total transverse energy, and at least two jets. The measurement uses proton-antiproton collision data at center-of-mass energy 1.96 TeV, corresponding to an integrated luminosity of 8.7 fb^{-1} collected with the Collider Detector at Fermilab during Run II of the Tevatron. We measure R to be 0.87±0.07, and extract the magnitude of the top-bottom quark coupling to be |V_{tb}|=0.93±0.04, assuming three generations of quarks. Under these assumptions, a lower limit of |V_{tb}|>0.85(0.87) at 95% (90%) credibility level is set.